It's something he's taken into consideration. But he's trying to give him the benefit of the doubt. This Frank, at least, appears to have some sort of closure that the Frank from his world (universe?) didn't have.

And if this Frank decided to take up the Punisher mantle here, then, well. What else is Matt here for?

But there's no time to think about that because there's a warm, soft muzzle against his hand and Matt lets out a startled laugh. "Uh -- hello." Very carefully, he traces his fingertips along the creature's nose, up to her ears. Definitely don't feel dog shaped. "She can come in, too. If she doesn't breathe fire."