well I am a mycologist by trade, so I won't sugar coat it for you.
you have a live, living organism living inside of your strap, and it's eating it.
it's digesting it. it's making holes in it, or rather pits.
you have to kill the organism.
that's why first, I would freeze it, and for a long period of time.
I would then soak it in acetic acid. I would leave it in the acid for a while.
this is probably going to ruin the finish if there is one.
I would then dry it out in my wind tunnel, lol. which in your case you can set it
on top of an old tv or modem or something. sit it in front of a box fan for a day.
whatever, dry it out.
then back in the freezer for another two weeks just to be sure.
when it comes out, I would clean it with the orange lexol, then clean any residue.
then I would condition it with the brown lexol, and again dry it.
then maybe some neatsfoot oil, but probably not, mold likes to eat that too.
anywhere that has slightly damp, still air will promote mold growth.
I suggest ceiling fans, moving air, dehumidifiers, that stuff.