Just shoo it away in whatever manner you feel acceptable. It's only a pigeon...& those are just rats with wings. Nasty ass things.
A few months ago, I had a pair of stubborn & ballsy doves casing my front porch for a nesting spot. I told 'em to shoo at a loud volume multiple times (which failed miserably) I threatened them, I finger wagged, I even threatened I would find where they live & kill them if they didn't GTF off my porch, well...they must've had a ball laughing at my expense, when not 2 days after that, I find 'em both in my back yard nesting an egg inside a flower pot set off the ground just underneath my office window.
I went ahead & cut 'em slack & didn't shoot a few bb's their way because I made a stupid promise to a woman I like to hang out with & she likes to think of doves & pigeons as separate animals even though she admits the only difference tween 'em are the words themselves.
The things people do for the coochie. Amirite?
Anyhoo, get rid of 'em or don't...if you don't, they will simply just leave when the egg is strong enough to fly...In my case, I was surprised at how fast it was. I didn't mark it on a calender or anything, but it seemed like all three of 'em took off in less than 3 months