The screw terminal block is literally the end of thousands of feet of phone company cable. If you go poking around in there you will find numbers that dont belong to you or anyone in your building (or at least you could have back in the day when people still ordered pots)

To clean up that part you should just look around the room and see if the metal covers for it are sitting in the corner. It's not your property or concern really. The demarc is the 66 block and if your active numbers arent in there you can call the phone company and raise hell that you dont even have an rj11 jack to do your isolation testing at, much less tagged jumpers.

It would be faster to just get your butt set out and test all the jumpers you got between the terminal and 66 block, cut ones not in service and pull them, then pull that off any others that those jumpers were servicing.

Your phone room is pretty good tbqh. The 66 blocks with the building cable on them are particularly nice. Dont worry about any of them. If you're putting a phone in for someone's desk just find that cable, theres probably a Jack there already, put tone on it then find it on the building 66 block.