In your head canon, where did the turncloak mercenary Tyroshi swordsmen go?

According to GRRM:

Second; what did Robb do with the Tyroshi sellsword who dipped his banners at Riverrun?

I don’t know what Robb did with him… but =I= forgot all about him, I blush to admit.

Now that you’ve reminded me… I imagine he kept most of them with him when he went west. Having just marched through the westerlands when they were on the other side, they would have had a certain value.

I also would expect that he suffered some desertions… these men were not bound to him by oath or ancient loyalty, and there was plenty of plunder to be had…

So chances are they left his army after he got back to the Riverlands, when they found out about the Blackwater and thought they might as well get out while the getting was good, before Tywin and his new Tyrell reinforcements could wreak his vengeance on those who betrayed him.