In addition to Reg Joo's suggestion, you could probably run an RG-11 cable from the internet connection (with a double-female if all they give you is a cable with no outlet - I can't tell if that outlet is live of not) to under the countertop, then get the box off the wall and mount it inside the cabinet. (As long as it doesn't get too hot in that cabinet in the summer.) Or you could run it to the basement or another room. (And shoot the supposed-technician who installed things that way. Back before the break-up, when it was all Bell System, anyone installing a phone that way would get fired for total incompetence. We ran wires into hidden spaces as much as possible. [My kitchen wall phone had no wires showing - they ran through the subfloor and footer, through the kitchen wall, then out to the phone jack, which was covered by the phone. And, no, I didn't do it myself, I was at work when my wife watched the installer working at home.])
There's a right way of doing things, a wrong way, then there's the easy way, which is "wronger than wrong".