Should I caulk over grout where the bathtub meets the tiles
Mouldy material should be completely removed - sometimes there is more mold behind it.
The tub should be filled with water before caulking in order to avoid pull forces. Push forces are less problematic to caulk.
A slope of 25 degree or more prevents standing water on the surface of the caulk, which is a frequent reason for mouldy caulk.