Why does the ball carrier not get penalised for it?
Surely the ball carrier shouldn't be allowed to grab the shirt of the defender?

As far as I can see it's always because the ball carrier has grabbed the tackler's shirt. What else is there to grab?
The ball carrier is allowed to fend off a tackler and a tackler is allowed to push his hand/arm away but to continually "rabbit punch" the ball carrier's arm suggests he has hold of his shirt.

I'm gonna be watching like a hawk for the next instance, then!

He's allowed to grab the shirt prior to the tackle being called complete. Most of the time we see these attacks at the arm on upright tackles when the ref hasn't called held yet, because the defender is satisfied his teammates are going to finish off the tackle, so he wants to get back in the defensive line.

If the attacker carries on holding the shirt after the tackle is called complete, then it is a penalty. That doesn't really tend to happen though because at that point the attacker wants to play the ball as quickly as possible; grabbing onto a defender who wants to get away from you makes that harder.

Thanks

I'm not sure of any positives in letting an attacker grab the shirt of a defender and it only makes the game look ugly & Messier when the defender is trying to remove himself from the Tackle and Slows the PTB down. Also leads to frustration between the two players/teams.