I suspect this is an inconsistency in what Tolkien wrote. But let's see how we can work it.
The full passage from Letter 297 is this:
(The attempt of Earendil to cross Ear was against the Ban of the Valar prohibiting all Men to attempt to set foot on Aman, and against the later special ban prohibiting the Exiled Elves, followers of the rebellious Fëanor, from return: referred to in Galadriel's lament. The Valar listened to the pleading of Earendil on behalf of Elves and Men (both his kin), and sent a great host to their aid. Morgoth was overthrown and extruded from the World (the physical universe). The Exiles were allowed to return - save for a few chief actors in the rebellion of whom at the time of the L.R. only Galadriel remained.‡
The footnote says this:
At the time of her lament in Lórien she believed this to be perennial, as long as Earth endured. Hence she concludes her lament with a wish or prayer that Frodo may as a special grace be granted a purgatorial (but not penal) sojourn in Eressëa, the Solitary Isle in sight of Aman, though for her the way is closed. (The Land of Aman after the downfall of Númenor, was no longer in physical existence ‘within the circles of the world’.) Her prayer was granted - but also her personal ban was lifted, in reward for her services against Sauron, and above all for her rejection of the temptation to take the Ring when offered to her.
Tolkien's views on Galadriel seem to be different at different times. Galadriel's degree of involvement in the 'rebellion' itself is questionable, depending on what you mean by 'the rebellion.' Galadriel did not participate in the Kinslayings and did not follow Fëanor to Middle-Earth. The nature of Galadriel's rebellion is a little different.
Galadriel was ‘unstained’: she had committed no evil deeds. She was an enemy of Fëanor. She did not reach Middle-earth with the other Noldor, but independently. Her reasons for desiring to go to Middle-earth were legitimate, and she would have been permitted to depart, but for the misfortune that before she set out the revolt of Fëanor broke out, and she became involved in the desperate measures of Manwë, and the ban on all emigration.
This seems somewhat whitewashed, compared to other letters, like the one you quote, or this one:
In Letter 320:
I was particularly interested in your remarks about Galadriel..... I think it is true that I owe much of this character to Christian and Catholic teaching and imagination about Mary, but actually Galadriel was a penitent: in her youth a leader in the rebellion against the Valar (the angelic guardians). At the end of the First Age she proudly refused forgiveness or permission to return. She was pardoned because of her resistance to the final and overwhelming temptation to take the Ring for herself.
Galadriel herself did tend, to non-Noldor, express that she was to some degree wrapped up in their flag:
‘Near,’ said Galadriel; ‘save that we were not driven forth, but came of our own will, and against that of the Valar. And through great peril and in despite of the Valar for this purpose we came: to take vengeance upon Morgoth, and regain what he stole.’
(The Silmarillion, Of the Noldor in Beleirand)
But in her heart of hearts, the reason she left was this - and I think this is the crux of the matter:
Galadriel, the only woman of the Noldor to stand that day tall and valiant among the contending princes, was eager to be gone. No oaths she swore, but the words of Fëanor concerning Middle-earth had kindled in her heart, for she yearned to see the wide unguarded lands and to rule there a realm at her own will.
(Silmarillion, of the Flight of the Noldor)
So while Galadriel was the enemy of Fëanor, her reason for going appears to have been 'I want to great and powerful and lord it over people', which doesn't seem that legitimate. 'Independently' also seems like a big word, since she is elsewhere said to have traveled with Fingolfin and the others in his train who crossed the Grinding Ice. (Though note that in one contradictory half-formed essay in Unfinished Tales, Galadriel and Celeborn, there conceived of as being from Valinor and not Middle-Earth, sail alone together from Valinor to the Havens.)
The fire of their hearts was young, and led by Fingolfin and his sons, and by Finrod and Galadriel, they dared to pass into the bitterest North; and finding no other way they endured at last the terror of the Helcaraxë and the cruel hills of ice. Few of the deeds of the Noldor thereafter surpassed that desperate crossing in hardihood or woe.
(Silmarillion, Flight of the Noldor)
she had dreams of far lands and dominions that might be her own to order as she would without tutelage.
(History of Galadriel and Celeborn, Unfinished Tales)
I think that the way this should be interpreted is that Galadriel participated in a separate, but related rebellion against the Valar: she ignored their commands to not go to Middle-Earth, and then their command to return (which in some sources is actually a continued ban!). And she did this because she wanted to be a great Queen.
But the moment she rejected the One Ring, she had essentially abandoned her cause and joined that of the Valar. So for an in-universe answer, Galadriel, as someone familiar with the Valar, must have expected the mercy of the Valar, without actually having experienced it yet.
This is supported by Unfinished Tales:
[Things didn't change until] two long ages more had passed, when at last all that she had desired in her youth came to her hand, the Ring of Power and the dominion of Middle-earth of which she had dreamed, that her wisdom was full grown and she rejected it, and passing the last test departed from Middle-earth for ever.
I think that's the best we can do while sticking to the text.
In Christopher Tolkien's opinion, we are in fact dealing with a continuity error here:
This statement [your quote], very positive in itself, does not however demonstrate that the conception of a ban on Galadriel's return into the West was present when the chapter ‘Farewell to Lŏrien’ was composed, many years before; and I am inclined to think that it was not (see p. 302).
It is very notable that not only is there no mention in this text of a ban on Galadriel's return into the West, but it even seems from a passage at the beginning of the account that no such idea was present; while later in the narrative Galadriel's remaining in Middle-earth after the defeat of Sauron in Eriador is ascribed to her sense that it was her duty not to depart while he was still finally unconquered. This is a chief support of the (hesitant) view expressed above (p. 295) that the story of the ban was later than the writing of The Lord of the Rings; cf. also a passage in the story of the Elessar, given on p. 323.
This makes some sense, since Galadriel's lament is actually very vague and she appears to be quoting a song about the original Hiding of Valinor. In Tolkien's original conception, no such ban may have existed at all, and it was simply Galadriel's own pride that kept her from leaving; and so we end up with texts that are somewhat contradictory.