You can try Surecrete SCR. We use it to clean new and old concrete. Be sure to read the instructions before using, as the dilution ratio is important.

@Urban West Design It is stronger than citric acid. I think that might erode the acid stain.

I would try keeping it wet for about 24 hours....maybe put a sprinkler on it, then see if the vine pieces have softened enough to come off with a brush. If it was Boston ivy, those little "feet" have some sort of glue in them to allow then to climb even on glass, and of course rain doesn't wash it away. But perhaps the sticky bits are dry enough that they will absorb water and soften.

You might try some sort of solvent....maybe mineral spirits....maybe denatured alcohol. Test on a small spot to be sure it doesn't also remove the paint shading.

@linda campbell I actually left this in a tub of water for 48 hours with minimal effect. I then added vinegar and left it for another 48 hours. Some comes off but it is painstaking work one little vine mark at a time. There has to be a better way.

Next I can try paint thinner. If that does not work then I am ready to try citric acid, but that could go very wrong if I leave it unattended.

I can report that bathing the acid stained concrete in water with vinegar added definitely reacted with the acid stain in a way that significantly deteriorated it. So that is not the solution. Still looking for a way to get this thing clean. My next step may be a pressure washer.

I think it looks nice just as it is. I wouldn't do a thing! I just bought an old concrete bench at an estate sale last year that is very worn and old looking.

@Richard Dollard "Just let the vines come off with time" is starting to look like a good solution :)

Pressure washing would probably do it. Even old concrete would probably be safe with that. when my husband uses a pressure washer on my sidewalk and turns out very nice and gets rid of a lot of stains.

@Dena Anthony I did not buy the pressure washer, so the experiment remains undone. I am sure that would take off the ivy, but I am unsure whether it would have also peeled off some of the acid stain.

I would say the vines won this battle. :) I tried nearly everything else on this and did not make significant progress. The vinegar did make some impact on the vines, but it also permanently stained/eroded the acid stain.