Mamma Robin & her eggs

My first impression is that Mama knows best. Why not give it more time?

Neologist is right. If the eggs are not viable she will give up when she's ready.

If there's no real problem with leaving things as they are until the season is over, maybe best to just leave it be. If it's ugly-looking it's easy to explain to a guest that you are hosting a robin family for the season. Actually that makes the subject an attractive conversation-opener (art least among animal-lovers).

I'm not sure how long it takes for robin's eggs to mature and hatch (maybe it's mentioned on the Wiki), but I would give it some time. They might still be viable. Daddy Robin is probably doing all the hunting and shopping, bringing home grub for Momma at time when you just don't see him.

At any rate, when the summer is over and the robins depart the nest, you can get rid of the old umbrella. They'll find a new place to build their nest next spring.

Grub is probably a very good choice of words, here.