My knock out roses has this mildewy-looking webbing on some of the flower buds. What is it? How harmful is it? Should I cut off the buds that have this? What should I do? Please help. Here's a picture of It:

Outdoors? Little spiders.
Indoors, likely spider mites.

It's an outdoor plant.

The buds that have the webs are deformed. Is there anything I can to correct this? Will this spread? Not sure what to do.

If it is spiders, they are drawn there looking for aphids to feed on. Aphids would suck the juices from a bud leading to a deformity.
If it is false spider mites, they spin webs and suck the juices themselves.
You could sprinkle a 'rose dust' insecticide on the buds. You could spray with Bayers 3in 1. 3 applications, a week to 10 days apart.
You could spray with diluted Neem Oil. Again, 3 applications. Once under control a once a month spray as a precaution would keep the vast majority of insects away.

The photo looks like there is some caterpillar droppings in the webs, but I would agree that it is typical spider webs, and has nothing to do with the bud damage. Doesn't look like any mite damage I've ever seen. Spiders are the good guys in the garden, as they eat the bad guys.