They didn't "give" anything, nor did they order Israel to remove the sites from their heritage register. The site had been used as a mosque in the past. Israel decided to add it to their heritage register only this February. In response (and do to the fact that the building has also been used as a mosque in the past), some Muslims successfully lobbied UNESCO to list the site in THEIR register as the "Bilal Bin Rabah Mosque/Rachel’s Tomb". Ie, recognizing both identities of the building.
This has nothing to do with current function of the building, nor telling Israel what they can and can't list on their own registers. It's merely UNESCO updating the HISTORICAL identifications.
Twisting the truth and exaggerating stories like this worked well 20-30 years ago. In the digital age though when specific details can be verified within minutes, it doesn't bode so well.