What did Schlage tell you to do? Do that. Simple. Done.

They said those circular strikes are not packed with the F-series Manhattan knobs-which have the standard rectangular. Also mentioned builders use the circular strikes since they are easier to install. We mare having a hard time finding smaller strikes and since it’s not on the door jam it’s completely sticking out.

It looks like the round strike doesn’t sit into the mortise, how does the builder consider that “industry” standard? Can you replace it with a ordinary rectangular strike or is there some damage we can’t see?

Why don't you get the proper strike from Schlage?

Would installing the rectangular strike cause more damage to the door frame?

You can get strike plates in all different sizes, so I'm sure you could find a regular rectangular one that will cover over the whole area (and require you to chisel out some extra wood to fit it in).

Maybe look into getting an adjustable strike plate so that you can fine tune the fit after the plate has been screwed in.

Find out if Schlage sells parts. Then buy the proper sized strikes. Pretty bad that your builder is cutting corners like this.