I know that when the ball is shot in a try for goal team control is eliminated, so I'm wondering if the ball goes off the rim into the back court, can team A(team last in control) legally recover it??

If you "know that when the ball is shot in a try for goal team control is eliminated," then why are you "wondering if the ball goes off the rim into the back court, can team A(team last in control) legally recover it?" :)

You've already answered your own question.

So i'm guessing there is no violation, right??

Correct. There is no violation.

If in the rebounding action, you deem A player to dribble or hold the ball, then that act constitutes player control and team control. The ball subsequently forced into the BC and then touched by A is a violation.

You got it! ;)