I myself wondered about this for a while and have come up with a few possible reasons.
The suit was based on Monica's t-shirt
The suit was based on Monica's t-shirt which was red, blue and had a star on it. As such it seems likely that Carol kept the star as a reference to this as well as the other reasons.
Click to enlarge and see the full image.
She does "alter" it... sort of
Perhaps quite importantly, she does alter the colours of the suit around the logo to make it look like the logo extends onto the suit further than before hand. See the gold strips to the side of it on the new look compared to the old:
Click to enlarge.
Click to enlarge.
The Starforce uniforms are personalised
We can see in the above image that each member of Starforce has a slightly different uniform. As mentioned in this excellent answer the stars on each person's chest are also tailored. This was indeed a conscious design because each member is unique and has their own weapons as Sanja Milkovic Hays states below in Marvel's Captain Marvel: The Art Of The Movie.
The Starforce uniforms are similar in design and color scheme, but each has unique detailing. "They were designed on the Captain Marvel costume," Costume Designer Sanja Milkovic Hays says. "Her costume is almost the same. It's just a different color, black and teal, and then everybody else's are similar. But each costume is unique because they are a specialized force, and each has his or her own weapons. Each costume has a different star. Each has slightly different lines, different shoulders, different weapons. I think for all of us, the first time we saw Starforce, it was like, 'Oh my God. This really works.' It was just really amazing."
Was it possible?
It's also worth pointing out that as mentioned in Stark07's answer the suit itself probably didn't have the in built functionality to be able to make physical changes, it only appears to be able to change the colour of the suit. Therefore, she would probably have had to make the modifcations by hand rather than through any built in process.
However, there are two things that could be evidence against this theory. The first is that her helmet comes out of the suit so maybe it can make modifications on the fly. Of course this is easily explained by this being an in built function though.
The second and perhaps more important thing though is that we do see her change the appearance albeit ever so slightly of the suit as mentioned below. She adds gold bands at the side of the star which do look slightly different to the bands that were there previously.
Was there time to?
The mission wasn't exactly time critical but it did need to be done quickly. Carol didn't exactly have the time to play around with such an unimportant part of her suit, changing the colours immediately sends the signal that she's changed. Further changing the symbol wouldn't have affected that much.
If I'm remembering correctly when she actually decides to change the colours she's just about to leave so there probably wasn't time to take the suit off and remove the logo.
Was it needed?
As mentioned above changing the colour of the suit sends a strong signal that she's changed alliances and so changing the symbol wasn't actually necessary.