Cleaning grout under caulk line (between tile and tub) before re-caulking?
There isn't anything wrong with grouting between tub and tile given that you do it right.  I fill up tub full of water (weight) and grout.  I feel grout is just easier to deal with.  My grout has lasted 6-7 years now in one bathroom without any sort of cracking or separation.  If there was separation I would caulk it.  

It does get mildew and mold and I probably spray it with cleaner once every 4-5 months.   That is about it.  

From what I can tell from your pictures, that doesn't seem like grout.  And if it was grouted it was done very poorly.  That looks like a mastic or even a white thinset to me.  And then caulked over.  It also looks like too big of an area to caulk.  I would suggest trying to break out some of that area and then going over it with grout.  (Also it looks like crappy caulk.  I would use silicone here)