I figured it out! It actually wasn't too hard. I got the source from https://www.xm1math.net/texmaker/download.html, then edited texmaker-4.4.1/completion/completion.txt to remove the terms I don't want.
After that, compile from source! I've only compiled from source a couple of times, and never for a program I already have installed. I need to check how to do this cleanly, then I should be good to go. I'll update when I figure that part out.
EDIT: Okay, it looks like the right way to do this is to just sudo apt uninstall texmaker and then compile from source. The source for texmaker provides a handy BUILD.sh, but the Qt Toolkit is required to compile texmaker.
So I went to Qt's website, registered, and started installing the open source version of Qt (it's a whopping 11G download!). Once that's done I should be in the clear.
EDIT: I just realized I needed to backup my user-defined autocomplete dictionary. It was easy but I would have been SO SAD if I had forgotten to back this up before uninstalling.
EDIT: Compiling from source is always an error-googling test. I successfully found 4 or 5 missing dependencies so that I could compile, but finally ran up against an error that seems to be a conflict between the old code in TexMaker 4.4.1 and the newest version of Qt (5.14). So I gave up trying to get that to work and instead did the fix to the latest version of TexMaker (5.0.3).
All I did was copy completion.txt to somewhere else and empty out the completion.txt in the source code. That way there are no hard-coded autocomplete entries. Then I modified the contents of that completion file to match the format in my settings backup from earlier, and all the default completion entries were imported as user-defined completion.
Works great, and now I have full control! Also I'm kinda glad I was forced to upgrade to the latest version of TexMaker, the one I had was ancient but I procrastinated upgrading because I didn't want to break my workflow (Math grad school is hard enough as it is!).
Editor\UserCompletion=part, containing my own commands). I already tried to remove some auto-completion commands from .ini, but nothing changed :-(. Would you have any idea maybe? – Watson Jan 17 '21 at 09:50