If it has a damaged surface just pull and replace (expensive but lasts longer...do acrylic and set in spray foam or plaster of paris) but if surface is okay use caulk remover to get the caulk softened between the tub and surround.

I also have  year around pest control, have the units sprayed once a month, every month, annually. 4 months of ownership  and i have already had 2 of my tenants resign their leases.  

https://www.amazon.com/WD-40-Specialist-Rust-Release-Penetrant-STRAW-SPRAYS/dp/B00631GQGW/ref=sr_1_1_sspa?

But I also know that most consumers out there don't care if there is 1" closed cell spray foam on their walls and that we used fiberglass composite windows vs vinyl windows and the list could go on, but these are things that I care about.

I had 3 military pilots as tenants and they kept spraying mildew remover and wiping the mold off the walls and didn’t tell us until it became a huge issue.  

I am currently spraying it with Enzymes and then plan to pour as much Kilz in this spot as I can. 

Turned out it was his washing machine hose had decayed and sprayed my wall.

There were some gaps with spiders I recaulked and sprayed for spiders before moving into the vacant unit.

One of the upstairs bedrooms had this sticker on the wall.In the basement and the garage it appears that they sprayed white paint of some sort on all the surfaces. 

If your basement freezes consider insulation for the box sills (the area where the frameing sits on the concrete our block wall) - spray foam is usually the best as it will create an air tight seal and as a nice side benefit it also keeps bugs and spiders out.