The git-er-done in my mind would be the mesh strip underneath, glued to the adjoining wide sheet to connect your strip. Some packing tape on the floor beneath would keep the adhesive from sticking below to the foundation.


Now if I wasn't rushed, I'd pull it all out and slide toward the door in the background by the proper amount  so you have the wide strip at the entrance where your gap is. 
You will have to use a new strip on the back side of the register (toward the door) since the cutout will be exposed, but everything else, especially the angled section to the right will just need to be trimmed shorter.

Linda looks like you could get away with two new strips (at the register and the wide piece to fit in at your gap).