Id soak it in warm (not hot)water, perhaps leave a soaking wet sponge over the affected area for a while, wash off any egg remains and if any is left, repeat...
I would have though it' come off the paintwork fairly easily after a soaking,No?
It's been on there since last night, I haven't actually seen the car yet.
When the other car was done last summer I never got all the egg off the paintwork and that was with washing it with warm water within an hour of it being done. Suppose it had the sun to help with the drying on process though.
It hasn't rained since last night so hopefully it'll be OK