Caterpillars don't lay eggs. The adult moth or butterfly does, these
eggs then hatch into caterpillars, which change into crysalises, which
then hatch into moths or butterflies.
Frankly, if I see a caterpillar on my apple tree I am interested in it
and look it up in a book to find out which moth (usually) it will turn
into eventually.
I would avoid killing at any cost, but then that is just me!