Small collection on report, and buying a home

In may I moved and had a $700 utility bill that I was not expecting and couldn't pay. I didn't have a job yet so I figured I'd pay the late charges when I got one. Over the summer got a notice that it moved to debt collections.

..didn't find a job until Jan. I'm finally in a position where I can pay it and it just showed up on my credit report. I went from 762-642. I'm buying a house this summer and feel like this $700 bill just got way more expensive.

So I'm looking for some advice. I can pay the full amount today.

Do I call the deb collector and try to get pay for delete?

Do I work with the utility company? Will they get rid the report?

What impact will a 642 vs 762 have on my mortgage rates?

It's legit debt that I owe and I would honestly pay a little extra to just make it all go away. I've been stressing about this all week and have no idea what to do. I understand all of this is my fault, and it appearing on my credit report is exactly why a report exists but I just wanted to reach out and hear what advice was out there.

Thanks so much for your time.