You need to remove it and apply new caulk.
Grout should not be used where the tub meets the wall or floor. It will always crack. Tub moves and shifts. Should use caulk. Remove the grout and apply caulk.
Yes, William is right that grouting and caulking are not the same, and do not have the same functions.
Here is how to caulk around the tub: https://www.youtube.com/watch?v=eEsy7luzUTI