Why?

People had less technology but where not less smart than today. If all, they where used to be smarter than us actually because they had less tech.

Its just paper towels, that pull out one after the other with a stupid fold trick. Anybody even 600y ago would spot that after a brief looking at it.

No, they would probably be curious about the paper itself, but that would be it.

The fact that medieval times where "dark" its a 19th century invented lie. Actually, it's one of the most vibrant and brilliant times of all ages, where economy thrived and people grow was substantial (until 14th century climate changes and pestilences), low population had many advantages and drawbacks. Old roman technology kind of disappeared but the society overall was far from "dark" at all.

I'm more intrigued as to why, out of all things you could pick to bring back to medieval times should you have the opportunity, why would you pick a Kleenex box

Due to the super freaky time traveling probably. To be expected I guess.

Or that it was a holy relic you’d brought back from the Crusades.

It depends on place & time & audience. Most places weren't into witches thing and educated people would recognize it as a new material not something magical.

You would be considered a spy for appearing out of nowhere while not talking the language, probably.