This may help, https://www.jaguarforums.com/forum/attachments/xk8-xkr-x100-17/21168d1341788260-need-remove-rear-bumper-jtis-2004-rear-bumper-cover-76-22-77.pdf
Here’s one £46, https://www.britishparts.co.uk/jaguar-parts-c11/jaguar-xk-xkr-1996-2006-c45/badges-decals-c145/badge-trunk-lid-p1335
Tis the cheapest I can find.
It is quite possible given the recent hot weather and any moisture within the vehicle. If it doesn’t smell of mould then it may just require a good clean.
I would, however, pay particular attention to the door and window seals.😊