The door latch doesn't latch anymore so I need to replace it.
Cole Sewell storm door latch
That part is called the keeper. Fortunately, the 40-117 does come with a new keeper that you can install on your door.
So I bought the 40-150 which was miore expensive than the 40-177, which comes with a keeper because I got that message after I already ordered. Now, my contractor says the handle is fine but I need an extender behind the keeper I have (old one) and behind the handle so the door will actually latch.
Do you have something like that and do you know what he means?
Sure, it sounds like your contractor is saying the keeper has to be packed out a little to meet the handle. If so, you could just use a couple washers. We don't have anything specifically meant for that purpose but I've used washers in the past and they work great.