Do you know how much fertilizer was applied? What type of fertilizer and the size of the yard? Normally when too much fertilizer is applied you will see deep green tall areas around the dead area. You will also see the path they took with the spreader. This doesn't look like fertilizer burn to me.
How long ago was the application? Do you know the grass type? Was the crabgrass there before? How did it look before? What you want the end result (something green or augusta national)? Lastly, how much time, money and effort you want to spend on this (pick only two)?
I'm asking a lot of questions to help you formulate a plan.
I don't mind the questions. I appreciate the help. I'm not sure how much fertilizer they applied or what brand they used. I know it was a weed and feed type product. After it was applied they said not to water it for a few days to make sure the weed killer in the fertilizer has a chance to work. It needs to stick to the weeds otherwise you're just applying a fertilizer. The yard is 49' x 58' with a small walkway down the one side of the house.
Last year she had the ground in the back yard leveled and grass seed planted. The grass is mostly ryegrass and was very green. There were weeds in the grass but not a ton of them. It was enough to try and kill them before they started spreading. She also has a small dog that goes in her yard but I don't think he could do damage like that.
It's been about 3 or 4 weeks since it was applied. I noticed the damage started right after. I live in NJ where it's been humid and raining a lot the last few weeks and I still don't see any improvement. I'd like to keep the cost down as much as possible. It doesn't have to be a golf course, I'm just looking for something green that looks nice for her to enjoy.
I have another family member who works at a local outdoor equipment store. I could get a de-thatcher, core aerator, and overseeder pretty cheap... if not free. I'll be honest though I don't know much about lawn care or I would have done the work myself.