Is it Asian jasmine (Trachelospermum asiaticum), Cynthia?

I don't know if Roundup this time of year will work on anything. I could be wrong, but I think it needs to be sprayed on actively growing plants so the plant will take it from the leaves into the roots. This time of year, even evergreens are slowing down their growth to the point that they may not be able to do that enough to kill the plant. Also, you're supposed to spray Roundup on the leaves so it can be taken up by the plant. If you've already mowed the groundcover, there likely won't be enough leaves to do that effectively. That's probably why it didn't work on that holly.

How about covering the area with something impervious like black plastic or sheet metal to starve it of sunlight? I do that for bermuda and it works beautifully in just a couple months, though have never tried it on a shade-tolerant plant, so don't know how well it'd work on them. Other than that, the only thing I can think of to get rid of it is digging it out, something you'd likely have to do anyway since even if the Roundup killed it, the woody stems would still remain for quite a while until they rotted out (a year or two?).

Thank you

Yes! Asian Jasmine is it.
I have to lay a bed of sand, not a patio thing as I had thought. So, dig it is. The holly had put on some leaves and I poured it on them, but to no avail. Thank you for enlightening me and I'd better start digging soon.

smiles of appreciation
c

We used old roofing shingles under our pea gravel bed to keep groundcover from invading. That was a long lasting solution, just be sure to overlap so that there are no uncovered areas.

Pam