I don't understand what should be done, open a new hole in the wall higher up? Why install a vertical line? The pipe is already vertical...I think that I will have my contractor contact the plumber to get this resolved. We are paying big $$ for this installation...They also installed my new faucet which comes with a sensor for hands free turn off and turn on but installed the box that contains the battery etc way up behind the sink where I can't even access if I have to change the batteries.
Well, I am just sharing how I would install it for myself, how would fix it for a friend or family member, or especially how I would want it installed if I paid somebody to install it for me.
There are little niche boxes for things like washer machine hookups, fridge hookups, ice makers, etc that are installed in stud + drywall walls; which have the plumbing line come from underneath in the wall, up to about counter top height or a bit higher. There is no way to install such a thing with whatever lazy thing the " plumber " did. Things like that done by " pros " are exactly why I got into DIY 22 years ago. Now I do see that you have two lines going up. So, such a niche may not fit, depending on which one it is, and how much space it needs etc unless one has it in hand looks it over. But that's where a bit of length and going higher may help so the fat part of the niche is right at the space between the two pipes, since pex has a bit of flex when it is longer, allowing for some positioning adjustment, unlike rigid pipe.
The benefit of having it above counter height would be - if it is not encased between pantry and/or walls - to turn the water on off you'd only have to roll the fridge forward half a foot, instead of all the way out.
What you do is up to you.
Simplest thing. To close off the wall, one could potentially, turn that T-fitting forward facing the fridge and then turn the shutoff as needed, being that it is PEX. I'd be confident doing that with a brass T. I don't know how strong or delicate the plastic one is. But if that little shutoff were proud of the wall, you could just make-up two bits of drywall to patch around the pex. May need a slightly longer piece of pex on that line.