If you get someone a book for a present and want feedback on whether they liked/like it, do you say "Let me know how you like it." Or "Let me know how you liked it."
What's the difference between the two sentences here?
Both are possible. There is no objective difference.
The only difference is of temporal focus. If you say liked, you are setting the temporal focus at the time when they tell you, so that the liking is then in the past; if you say like, you are not setting any temporal focus.
In this case, I cannot think of any consequence arising from that difference in temporal focus, so I can't find any practical difference.