Hailey Davidson -- the transgender golfer aiming to make the LPGA Tour -- tells TMZ Sports she's very grateful for Caitlyn Jenner's support this week ... but she's striving to have a further chat with the former Olympian with the hopes that it will help "clear up some assumptions" going forward.
Jenner threw her support behind Davidson on Fox News on Wednesday, saying she believed Davidson -- unlike transgender swimmer Lia Thomas -- had no unfair advantage over her female opponents because "golf is a totally different game.