Bugs that leave small round green eggs could be a stinkbug. They lay there eggs together under a leaf in a honeycomb pattern.
Moths and stink bugs lay eggs in tiny clusters in the fall. The eggs are white in appearance and can be bunched with a hundred others.
Cabbage insects are one type of insect that lays tiny white round eggs under leaves. These bugs are usually found in gardens.
Almost all of them. If you found them in your house along the floor boards, they are probably cockroach eggs.
earwigs
If they are oval shaped and in clusters they could be ladybug eggs, they are a darker yellow color.
Many reptiles lay bright yellow eggs. Yellow eggs are often a sign of the eggs not being fertilized so many reptiles have this capability.
The painted tiger moth is an insect lays bright blue eggs. Most of the time they lay their eggs in shrubs so their baby caterpillars can start to feed right away.
Moths lay eggs on ferns.
The insect that lays small, hard shelled white eggs is probably an ant that is black in color. This type of ant is commonly called a carpenter ant. Carpenter ants like to lay eggs away from the nest in warm, damp places.
Some insects lay red eggs. The wolf spider is a common spider in North America that lays its eggs in clusters.
giant water bugs
It could be Ladybug eggs.
that would be termites
None do, what you heared or assumed is a myth.
An insect called Bed Bugs
Greenhouse Whiteflies are a pest that can occasionally be greenhouse pests. The greenhouse whirefly lays their eggs in a circular pattern.