Honestly, I think Tara would warm up to Jason pretty quickly. She definitely knows who he is, both as Red Hood and as Robin, because Slade clued her in on the whole family situation when she was infiltrating the Titans and she's kept up to date. She tends to gravitate towards people who are as jaded and bitter as her (Wally, Raven initially, Beast Boy, Rose), and she's calmed down from her meta superiority hot takes when she was a 16 year old.