Hey, @PrettyGranny!
Logitech and Linux has been a match made in stormy seas for some time. However, independent developers have done some good job trying to smooth the… waters!
I’ve had my share of Logitech mice in my life and right now I have a trusty G600. I did some research on your mouse and it does have some settings that can make its keys behave like a hamster on crack. So, you’re right to bring this up!
I found this guy in Netherlands who found a nice workaround with some free app on Linux, which I believe you can benefit from. I’m attaching the link below: 
https://dev.webonomic.nl/using-a-logitech-g203-mouse-under-linux