Chireaux....if the contractor said that the door should set below the lip, then I would let the contractor know that he screwed up, and let him fix it. Isn't he the one that scheduled the concrete guys? If so, they should be able to work something out.
The reason that I say this is that no matter what you rent, whether it be a concrete saw which is needed, or a grinder with a diamond blade, if you don't know what you are doing, it's going to look like a *********** of a mess. It's easy for a lot of people to say that "all you need to do is....". It's not that easy, period. With a concrete saw, it's hard to keep a straight line going, and it's hard to control depth. If you get a blade for your circular saw, you'll have the cost of the blade, and chances are that when you are done, you'll have a ruined saw ready for the trash. You will have a ton of dust unless you run water, then you will have a ton of slurry. And that is just for the vertical depth cut. If you can get that cut done with no problems, then you have the horizontal cut to take care of. They don't make a concrete saw to do that. So you either have to grind everything down to the correct depth, or you'll have to make a series of vertical cuts down, all to the same exact depth, then knock out the small rows between the cuts. And once you bust them out, some will break above your depth, and some will break below your depth of your cuts. So you will need to grind. And seeing that this is outside, you can't fill and epoxy over it as it will look very odd. And if you do nothing but knock out the pieces, then it will look like ****, even after grinding because this is what you will see at the bottom of the garage door.
So I would let the contractor deal with it, and if he doesn't, I would look into changing the seal somehow. If your window looks out of place because it is higher than it is supposed to be, then you'll have to learn to live with the looks of it. Sorry.
