This blog post from 2011 discusses Gimli and Feanor, and their requests of Galadriel, in a bit more detail. There's some comparisons to Aule's creation of the dwarves, as well as a reference to a letter that may perhaps contain an answer:

In a letter that invites us to see the exchange between Galadriel and Gimli against the back-drop of the earlier encounter between Galadriel and Frodo, Tolkien indicates that until Frodo’s arrival in Lothlórien, Galadriel had actually believed her own exile from Valinor to be not temporary but “perennial, as long as the Earth endured.” It was only after her intercessory prayer on Frodo’s behalf—that he should be allowed the grace Galadriel believed to be forever denied to herself, namely of returning to the West—as well as a reward for her refusal of the Ring and her part in the war against Sauron, that Galadriel discovered the ban placed upon her return to the West to be eucatastrophically and miraculously lifted (Unfinished Tales 229).

The post goes on to suggest that Galadriel gave him the hairs because, ironically, the dwarf didn't want the hairs as a physical thing for himself. Rather, he wanted them as symbols of new friendship between elf and dwarf.

This blog post from 2011 discusses Gimli and Fëanor, and their requests of Galadriel, in a bit more detail. There's some comparisons to Aulë's creation of the dwarves, as well as a reference to a letter that may perhaps contain an answer:

In a letter that invites us to see the exchange between Galadriel and Gimli against the back-drop of the earlier encounter between Galadriel and Frodo, Tolkien indicates that until Frodo’s arrival in Lothlórien, Galadriel had actually believed her own exile from Valinor to be not temporary but “perennial, as long as the Earth endured.” It was only after her intercessory prayer on Frodo’s behalf—that he should be allowed the grace Galadriel believed to be forever denied to herself, namely of returning to the West—as well as a reward for her refusal of the Ring and her part in the war against Sauron, that Galadriel discovered the ban placed upon her return to the West to be eucatastrophically and miraculously lifted (Unfinished Tales 229).

The post goes on to suggest that Galadriel gave him the hairs because, ironically, the dwarf didn't want the hairs as a physical thing for himself. Rather, he wanted them as symbols of new friendship between elf and dwarf.