[neatoman]

The TMNT characters in the Batman crossovers are clearly based on their IDW counterparts but there are a few elements that are off and clearly marking the crossovers as non-canon:

Karai claims to be Shredders daughter, which isn't really the case in IDW.
Shredder is put into prison for a while but there is no place where that would fit.
Baxter is mutated into a fly but in IDW he's clearly still a human being.
Krang seems to have tried to defeat the Turtles multiple times but IDW Krang was only ever in direct conflict with them twice if you don't count the trial.

And Uh... It's not a contradiction exactly but the idea that Bebop and Rocksteady would ever lead a faction of the foot is absurd in IDW. Not only are they incompetent idiots incapable of leadership, they're not even respected by anyone. Everyone else kicked them out of their organisation and the Foot only keeps them around because mutating them was expensive, Splinter even kicked them out when he was in charge.