If you can get over the "yuck" factor, share their food with them!
Take a small portion and put it on your "own" plate and (please) get your own fork, and have the meal with them. Some people eat better this way, or don't want to seem rude by eating in front of you. Also, some believe that the food is poisoned or otherwise dangerous or un-fit to eat, so this method works well with paranoid dementia.
Or try feeding them outside of the dining room. While they are sitting in a chair, suggest "a little tea while you visit." Prepare some small sandwiches and fruit cups, and other, light "tea-time" foods. Then have some line of conversation prepared and sit down and stay a while. This works very well with women, especially.
Especially important is that the food looks appetizing and is simultaneously easy to eat. Anything that has to be cut, like a big piece of chicken, or even just looks big, like a hamburger is much less likely to be eaten. Small pieces of easily chewed food are good. Try to avoid all the mush from running together though, because that looks very unappetizing!
Have them "help" make the food. Take the sandwich apart ahead of time and let them "make" it themselves. Bring dried oatmeal or fresh fruits and let them mix it in with yogurt, ice-cream, or pudding.
Just keep trying. Remember that they probably will not remember that you just offered them food 1/2 hour ago!
Good luck to you!