Keep it.

Fungal mycelia. Probably digesting the burlap :-)

Lovely.

The branching structure on this makes me think it might be a slime mold rather than fungus, possibly Brefeldia maxima. I have a slime mold living in my worm bin that is very fond of spreading out on burlap, although mine is bright yellow (probably your basic dog's vomit slime mold, Fuligo septica, which has also turned up in my garden now and again).

I can't think how it is that I don't have a slime mold field guide on my shelf. Must correct this omission...

Thank you all for the replies! It turned out that it is very sensitive to humidity changes. The most part of it disappeared the next day after opening the lid. There is still a small white piece on the lid, but I am intended to keep the worm bin uncovered for the next few days, so it will probably disappear completely.