Rather than eggs, more likely a fungus which is growing on the organic stuff in the potting mix.

Pyrethrin is a broad spectrum pesticide that should only be used as a last resort. You did start kind of with a good IPM program by asking for help identifying what you have, but the rest is are those causing a problem that needs to be solved and thus far there is no problem. Then if what you have is causing more of a problem than you can live with and needs control you start with the least toxic means of control and that might be hand squishing, maybe an insecticidal soap, maybe just encouraging predators to move in.
Don't just assume, as the pesticide ads portray, that every insect needs to be killed off.

Slide the rootball out of the pot and look with a handlens or powerful magnifying glass.

Quite unlikely it's an insect or its eggs. If a fungus in the potting mix, pyrethrin is wasted and *not* effective.

Even if it is eggs, you'd have to squish them to get rid of them.

I finally got my answer--these were soil mealybugs.

--Rr