Ceramic tile? I would start with a plastic scraper and then move to a scraper with a razor blade. You could add in some heat - gently - from a heat gun. Or, after scraping, Goof Off might get the remainder of the gunk. If you have fingernail polish remover with acetone, that might work.

What type of tile? Vinyl? Porcelain? Ceramic? Cork? Linoleum? Stone? Wood?

Does this bathroom floor have in-floor radiant heat? If so is it electric or hydronic?

What type of rug? What type of backing?

Please post photos of the issue.

if it's rubber goo on ceramic/porcelain tile, I agree with careful putty knife removal followed by Goo Gone. if it's some other combination, we're going to need more info.

GooGone and GoofGone are for removing glue but so will liquid Butane lighter fluid in the yellow plastic bottles usually in the check out aisle at WalMart and, if memory serves, it costs less per ounce. Not sure if the Butane would damage the tile but suspect the pro strength GoofGone may well be the same thing..

Goop or GoJo or Fast Orange are hand cleaners that help remove sticky garage kinds of messes. They have a bit of grit in them though. Worth trying if your GooGone or GoofGone doesn't work.

Would try Goop on the dry icky mess (don't add water) and after it sits a few minutes, then try to scrape it away with a non-scratch silicone kitchen spatula.

I have been able to soak the glue off a plastic medicine bottle with Mr. Clean -- may not be the same kind of glue.

Ordinarily I'd suggest trying alcohol if these products don't work since that can sometimes help remove ink and some kinds of glue but finding alcohol in stores now is difficult.

Nail polish remover would be the last result since it could damage the tiles -- but the milder kind might not.

Whatever you try, do try a small spot first and be sure the cleaning product it doesn't damage your tile before you put the product on the rest of the floor.

Good luck.