Withdrawing from project I am helping in I have been assisting with a project that my friend had come up with. I am doing the entirety of the analysis for it as they have zero research experience and are not able to do anything beyond conception of the idea.

They are not letting me submit it to a conference to present a small part of the project at a very small "conference" (quotation marks because it's a one day event held at a university auditorium for medical trainees specifically), based on the fact that they would like to present first. I have been slightly annoyed by this, and am contemplating withdrawing from the project, which admittedly is a bit of a dirty move.

That being said, if I do withdraw from it, could/should I ask for any and all analysis done by me to be removed and not used?

Or should I just bite the bullet and let them just carry on.
Withdrawing is a loss-loss situation and I will not recommend it. You have done your work and they seem to have the motivation to release it some day. If you withdraw now, the work is gone, tension arises, friendship threatened. These are not worthy for a short moment of revenge-induced pleasure.

If you feel your input is so instrumental then take this as a lesson to bargain better; in future when similar collaboration comes along, make "have the right to present at xxx conference [year/month/day]," or similar terms as your condition. You should also raise the issue of authorship from the get-go.

Ascending one more level, if you're indeed that much more experienced than the team in terms of how the research realm works, why not help them further? Connect them with this very meeting that you plan to attend, and propel the work forward by letting more people know about it.