Hi, Teatree! Welcome to NGA.
I haven't grown peppers, they need more heat than I have. And I only cured scale-like bugs once. (Yours MIGHT be aphids, but don't take my word for it!)
Those sure look like insects! I would use the hardest mist or a fine spray from a garden hose or irrigation sprayer to knock off as many as I could. You can also rub or knock them off with a soaked cloth or Q-tip, if you have infinite patience. Covering the soil and giving it a shower in your tub might work, but be prepared to call the plumber to unclog your drains if you're like me.
Then use an insecticidal soap spray, or just a soapy spray, with or without some rubbing alcohol. Soak it good to get into the crevices to kill young, small insects. Rinse after a while, depending on how sensitive pepper leaves are.
Repeat after 3-4 days (or a week?) to kill the eggs that hatched in the meanwhile.
I've seen wide ranges of concentrations suggested online, and some say "only use natural soap becuase it is fatty organic acids that kill", and others say "detergent is better". I don't which, or why!
Hopefully someone will comment who knows how sensitive peppers are to soap (and detergent, and rubbing alcohol) .
Some recipes cluster around:
one gallon of water
soap or detergent: 2 teaspoons to 2.5 ounces (???)
rubbing alcohol: 0 to 4 ounces per gallon
