I can imagine you would be freaked out! It’s flies you’d need be more concerned about.
If rats, then flies have gotten in between the walls, do ask the exterminator to investigate where they’re getting in.
For the room where you’ve put Frankie, make sure you block of access points where flies could get in. It’s the litterbox they would be attracted to, so clean more frequently until the issue is resolved. Also check his bottom often. If he’s got clean, dry fur, it shouldn’t be an issue.
The flies gravitate to damp, smelly areas or wounds.
If he’s in habit of leaving cecatrophes (the droppings they’re supposed to eat) remove those when you see them so they don’t get mushed on the fur.
You could put some fly traps, sticky papers etc in the room also. Out of Frankies way, of course! I hope you get a resolution soon. You must be grossed out! These things happen unfortunately. I have a lot of mice running about the yard lately. I don’t mind that so long as they don’t come into the house.