Hmm.... I just checked for available updates (under FF’s Help menu) on two different computers, and it says that version 44.0.2 which I’m running is up to date. Also, at Mozilla.org the latest version that is available for download, at least in non-beta form, is 44.0.2.
I’m wondering if the popup you saw was not from Mozilla.org (from whence Firefox comes), but might have been from some semi-legitimate or illegitimate third party, for the purpose of installing adware or spyware.
It may be a good idea to take a look at the plug-ins and extensions that are now listed as being installed in Firefox, and see if any of them are new. In which case you can select for them to never activate.
It may also be a good idea to take a look at the list of programs that are installed on your computer, under Start/Control Panel/Uninstall a Program, and see if there is anything that looks unfamiliar or suspicious, in which case you can uninstall it. Google its name in cases of doubt.
Also, performing a "system restore" to an earlier date **might** allow you to get rid of the update. (Type "system restore" into the search box that appears near the start button, when you click that button). That won’t affect any of your data files or email files, but you would probably have to reinstall any programs or Windows updates that were installed subsequent to the date at which the restore point was created.
Finally, if necessary you could uninstall Firefox, and then download 44.0.2 from Mozilla.org and reinstall it. I’m not 100% certain, but I believe doing that would not affect your existing bookmarks, Firefox settings, cookies, stored passwords, etc, which are stored in a profile folder that is separate from the program folder.
Best regards,
-- Al