Larry's link is a good reference. I couldn't tell from the Picture but I used a Metal Paint Scraper. Simply put, it's a single-edge, straight razor blade that's slid into a hand-held, metal sleeve. The blade can be 'extended and retracted' for use and safety. (It kinda locks in place in either position. It would be hard on the knuckles if it didn't lock in place!) I feel that the Razor Knife is 'harder' to hold 'flat/flush' along the tile/tub. That's why I don't use it.
Anyways, since it's a straight razor, you can slide/cut your way through the caulk flush up against the tile/tub. Buy a box of replacement blades too because you may 'like it' when the blade is really sharp. It doesn't take much to damage a blade. Since it's a 'flat, sleeve-like holder', it's not bulky at all like a Razor Knife that has a 'handle'. You simply slice down behind the tile along the entire wall, then you slice under the caulk along the entire wall, then you 'cut' the strip where you started, and peel it away.