More questions about wild pigeons in my garage

I got these two pigeons that made a home in my garage. Yes, they are
still in my garage! They are not locked in but they seem to want to
stay. I made their place uncomfortably small and they still want to
stay. They want to raise babies even in the middle of our harsh winter.
I got two wood eggs and fooled them through the winter. They just laved
two more eggs and I think that I can lock them out of the garage now.
Spring is around the corner. Any ideas? I have to do something fast!
What would happen if I let them hatch those two eggs? Would they go
away when the babies grow up?

No, they will not go away when the babies grow up. Since they were able
to successfully raise young, they would be more inclined to do it
again.
You should just lock them out of the garage and be done with it, but
knowing you, (Smile!) you will have to wean them from the garage. Lock
them out, but keep feeding and watering them outside for a few days.
Once they realize they cannot get back in, they will find other
accomodations. But be aware, that the first place they will look is in
the immediate area. Eves of your garage or house, or neighbors house.
But I know you like them, and would probably just like them to come by
and be fed, as opposed to having to clean up after them all the time.
But you might as well just give them a decent box/shelter that they can
live and raise young in. A 2x2x2 box with half the face covered is all
you would need, and placed in a high place where predators can't get
them. All you have to do is scrape the box out once or twice a year.
(If you have hawks and possibly owls around thou, you would need to
make the entrance small enough that only a pigeon could fit thru, with
an outside board that they could perch and sun themselves, but jump
into the hole if a hawk attacks.
If you do the box thing, don't lock them out of the garage yet. You
will need the enclosed garage to catch them at night, then place them
in the box, wherever it is located. If they like the box, they will
explore it in the morning and remember where it is. Matter of fact, I'd
put them and their whole nest with eggs in there.
I'll keep checking back here to see how you are doing ..
E-Man