Shower corner has grout covered in caulk
The grout, assuming the rest of the shower was installed properly, isn't the last line of water defense so it's probably fine to leave as is.  Grout is permeable anyway so it wouldn't be a good line of defense anyway.  That being said, you can leave it as is.

If you want to recaulk it then I would definitely remove the grout as the new caulk will not adhere well without more room.  They sell little hand-held grout removers at the home improvement stores and, in my experience, they're not going to do the brunt of the job.  You'll need an electric oscillating tool to get it done.  You'll also need ear protection because the echo in a shower will make your ears ring for a day (I speak from experience).  For obvious reasons you'll also need a mask.  Your electric tool will likely leave little bits of grout that you'll follow up with the manual tool.