Although the white debris pictured doesn't look like it came from an insect (we can't really see enough detail), even if it did, it's not a pest of concern. The other photo shows what appears to be leafminer damage, which is cosmetic only and doesn't cause serious damage to the plant. If you are harvesting the beet greens to eat, the leaves with leafminer mines are safe to eat and you can just cut out that injured portion. Information on management of leafminers on vegetables is included in the linked page. While too late for this season, in future springs, you can cover new plantings with insect mesh netting or floating row cover to keep the insects from accessing the plants, especially since you don't need the plant to be pollinated in order to get a harvest (as with, say, cucumbers).

Miri

Good afternoon Miri,

Hello Jeff,

Okay, we are happy to take another look, though this platform can't accept video files. (You could upload it somewhere and link to it, or try to send still images if they are not blurry.) Our primary guess based on the all-white appearance is a type of hopper nymph; either a planthopper or maybe a treehopper, both of which are fairly common on a variety of plants. They suck plant sap, but in this situation don't cause any serious damage and don't warrant control. (Plus, they run away from disturbance or jump so readily that trying to spray with them a topical insecticide like neem oil would not accomplish much.)

Miri