When there is a restraining line. Can the thrower bounce the ball inside the restraining line on a throw in. What about after a made basket?

Shont

It is a violation in either case. The restraining line acts as the temporary side line or end line for the purpose of the throw-in. So if a player bounces a pass that hits on his side of the end line it would result in a violation. Same is true of a restraining line. There is also no difference between a designated spot throw in or a non-designated spot throw in like after a made free throw. The same rule applies.

If by "inside" you mean on the playing court side of the line, then it's a violation.

If by "inside" you mean toward the playing court boundary line, then it's legal.

Bob,
Did you reverse those two or am I reading it wrong? I know you know the correct anser.

Bob got it right. The boundary line is part of "out-of-bounds." Similar to a player stepping on the boundary line during a throw-in (legal) and stepping over the boundary line (violation).

Z

Well, either direction could be right depending on the nature of the "bounce".

If the thrower is simply dribbling the ball, the bounce on the OOB side of the line is legal. A bounce on the court side

If the bounce is part of a bounce pass to a player on the court, it reverses. The bounce on the OOB side of the line is violation. A bounce on the court side of the line would be a leagal.