This is a film sealer, as opposed to a penetrating sealer (bare concrete, grout). I know of no solvent/stripper that will remove an acrylic finish that won't remove (or damage) a latex undercoat.
I would try a reverse progression of grits, until you get to the paint. You may need to wait weeks for a hard enough/dry enough sealer surface. Start at 600 over a sanding block. Only go rougher if you make no progress (320, 220, 120). Only sand enough to get TO the paint, then recoat with the sealer. If you have access to a sprayer, it will make blending the areas easier (to hide lap marks)
Clay Absorbent.
This stuff is available at most auto parts repair stores. Sometimes it is available at big box stores.
It is NOT the same as cat litter although it looks strikingly similar. The resemblance is so close that "kitty litter" is the 'street' name for this product.
However, clay absorbent is far superior in its ability to remove oil from concrete. For example, my father and I moved a broken 2.5 hp motor over a concrete walkway in a plastic tub. At some point the load became unstable and the engine tilted enough to force us to drop the tub. In doing so, we streaked the walkway with oil approximately 2" wide and 6" long.
Since I was away from home and he did not have any clay absorbent on hand, I promptly drove to purchase some and placed the product according to the manufacturers directions. After the second application was swept up, I made a third application and ground the product into the concrete with my shoe and left it to sit until the next rain washed it away (not recommended, but hey the walkway was pristine beforehand and my dad has a low carbon footprint).
To this day, there is a spot on the walkway that is cleaner than the rest. I am not exaggerating in the least when I say that the entire section now needs the ground-in-and-washed-off treatment to help minimize the white spot left behind where there was a dark black oil spot before.
Two applications should do for what you need. Skip the ground in trick unless you promise to recover the waste water ;)
Edit:// Just read where you said spots are old and kitty litter will not work.
Try the clay absorbent. It is about 100% more effective than cat litter on any day. Also, if it does not come up, leave it for a night or two.
Other than that, (using a test spot!!!) dampen the concrete with fresh oil (detergents good...) then place the oil dry over it and leave for at least a day. If all else fails, grind it in!
Best Answer
I had an entry way floor some 30 years ago that had old hard vinyl tile glued down in it with the blackish-brown type of adhesive. I wanted to replace that tile with a ceramic floor tile so I peeled out all of the old tile. I then used a wide razor scraper to get most of the old adhesive scraped off.
After that I purchased a few gallons of aggressive paint stripper, opened every window in the house, shut off all gas appliances and pilot lights and poured out a layer of the stripper across the whole floor.
I let it sit for a suitable time (may have been about a half hour or so). Then working some with a wire brush and metal dust pan as a scoop I took up all the goop off the floor.
Finally using a bucket and a large sponge I washed up the whole area with a copious amount of hot water to remove all the stripper residue.
After the floor fully dried the surface was the nicest clean concrete surface you could wish for. I was able to put down the tile setting cement and had no problems with it adhering to the concrete.