Try white vinegar and baking soda. read the link below
https://homeguides.sfgate.com/lift-stains-linoleum-floors-31358.html

Also search on YouTube.

MiMi, yes I've tried bleach and it didn't even fade it.

Have you tried Magic Eraser?

Are you sure the floor is linoleum and not vinyl?

Photos please.

Janice B, Yes I have tried magic eraser too!

I would try Citrasolv. It works wonders on so many things, so maybe this, too? I get it at Whole Foods.

Here are some pictures of the floor. The flooring is linoleum as it has a jute backing. I am currently trying a paste of Dawn dish soap and baking soda and the vinegar and baking soda mixture. Cross your fingers and pray that one of these work!

jellytoast, is Citrasolv similar to Goo Gone? If so, unfortunately, I tried that as well.

Just a thought. It’s a rental and the owner expects to replace, repair, repaint before they re-lease. Why don’t you call them and let them know what is going on. The flooring looks like peel and stick. This may not be a huge deal to them. Or offer them the offending rug!

No, it is not similar to goo gone. It is an all natural cleanser, degreaser, and stain remover made from orange peels. It is always what I go to first when something is giving me problems.