Can I patch and tile over a phone jack?
Yes, if the wire is out of service, remove the plastic panel, secure the wire with insulation tape and put your tile over it.

"Out of service" not connected to the main telephone system!

If it connected, but you have other PSTN jacks in the house, cut the wire ONE by ONE with insulated wire cutters!. Then insulate each wire with tape and finally the entire wire.

You will also need to remove the socket on the right, and then replace it when you done tiling, as the mounts need to sit ONTOP of the tile, and the plastic cover will hide the mounts nice and flush.

You could also leave a nice message for somebody in the telephone box, when they take the tiles down in 25 years, that it was a telephone wire.. or where you buried your gold treasure. Heheheh