hello dfwlms, this sounds like a problem possibly caused by adware already on your pc. please go to firefox > addons > extensions & remove the OfferMosquito 0.9 extension - it's rather unusual and might be malicious.
also go to the windows control panel / programs and remove all toolbars or potentially unwanted software from there and run a full scan of your system with different security tools like the free version of malwarebytes & adwcleaner.

Remove a toolbar that has taken over your Firefox search or home page Troubleshoot Firefox issues caused by malware

Your suggested actions have apparently solved the problem.

I went to the extensions to delete Moquito and there were no extensions there.

Spazzyone3,

If you have followed Phillipps suggestions above and are still experiencing problems then you may need to dig deeper using a malware removal program or tool. Because Malware is written for a different purpose than normal viruses, it is often not detected successfully by standard AntiVirus programs. Also, because Malware is generally given permission to be installed, it is considered to be a legitimate program and given a pass.

There are lots of great free malware removal tools out there and I recommend you check reviews on anything you are thinking about using, but my most used tools for this include Malwarebytes, Spybot Search and Destroy, Hijackthis and AdwCleaner (also HitmanPro but they are a 30 day trial). The first one will resolve nearly every issue and is a solid choice.

Since Phillipp already suggested this I recommend trying another name on the list as there doesn't seem to be any "one-size-fits-all" solution to these things and you may have to try several before being rid of the problem for good.

Good luck!

spazzyone3:

Thanks for letting us know you're having problems, however, please do not "hijack" other users' threads especially when they are marked as solved. Please start a new thread by going to /questions/new so we can give you support on your system, not based on another user's configuration.

NevadaJack:

I see you are a new contributor and I thank you for your answers. However, we have canned responses available at your disposal. These responses cover almost every topic here on SUMO. Please look at those and use those. We prefer new contributors use canned responses until they feel comfortable writing their own replies. You can find them at the top of the comment box with a hat saying Common responses.

Thanks for understanding!