Someone in the house who is not too bright accidentally flushed a
towel down the toilet. Kind of like a "hand towel" or a large
washrag. And they stupidly tried to use a plunger before realizing it
was a towel stuck in there.

Anyway, any ideas on how we can get the towel out? Is there some sort
of snake-like device with hooks or something that can grasp onto the
towel?

The other toilets work, so at least the towel didn't go TOO far.

You could try to snake it, with the goal of pulling the towel out of the
toilet, not through.
If you push the towel in and it gets stuck in the pipe somewhere, then
you're in more trouble.

That said, it's not easy to snake the toilet because of the built-in P-trap.

You may have to remove the toilet to get to the towel. Hopefully it is still
stuck in the toilet, not in the pipe.

Or you could try to find some chemical that dissolves cotton. It may take a
while.