It’s similar to a situation in the kitchen on my dorm’s floor, back when I was in undergrad, only less disgusting. Someone left a pot with the burnt-on remains of something to soak in September. It was still there at the end of April. Every now and then someone would take off the lid to check on how it was doing and no one else (including me) was willing to touch it to dispose of it or at least put the lid back on so we wouldn’t have to look at it. Plus even though it seemed to be abandonded, I didn’t want to risk pissing off the owner of the pot by throwing it in the garbage. I’m guessing the same person who took the lid off from time to time also put it back on, but I can’t be sure.
Compared to that, I’ll take a two-week-old stick of butter any day. However, even if you do want to see if the paper towel gets changed, you may want to throw it out by Friday, just so it doesn’t descend further into the “so disgusting no one is willing to even think of touching it” category.