Hi George.
My software is a text editor that uses ncurses extensively and has extended features for iterm2.
It is the same app that you fixed iterm2 to do italics for, many many years ago. :-)
If the terminal is iterm2, then I have hooks to do other iterm2 features such as changing the cursor between block and vertical line while inserting text.
I use ncurses mouse handling to add vertical scrolling. See man getmouse. In the MEVENT word, besides the documented BUTTON_ events, there are also undocumented events for scrolling up and down. I return these to my app as MOUSE_SCROLL_UP and MOUSE_SCROLL_DOWN and these are a joy to use while moving around coding text. You can scroll up and down in text by line or page. This is with the Magic Mouse upper scroll surface.
When left and right scrolling started changing iterm2 tabs, the thought jumps out to do left and right scrolling within the page of text in my app. It would not matter that these are not in ncurses : I am pretty good at writing hooks around that.
However as soon as I saw that to turn off left/right swipes is in Macos > Settings > Mouse, as Richard showed, then I realised it may not be controllable by iterm2.
If it is not easy, then at least I asked and it is in the iterm2 suggestion box. Thank you for listening. :-)
Cheers
-Greg.