reset has its place, but clears your screen. If you are running xterm or anything compatible, the shortest, least intrusive thing to use would be
printf '\033[?9l'
That is not explicitly stated in the Mouse Tracking section of XTerm Control Sequences, but xterm allows you to reset (disable) mouse mode by turning off any of the possible modes that might be turned on. Those are documented as named constants:
#define SET_X10_MOUSE 9
#define SET_VT200_MOUSE 1000
#define SET_VT200_HIGHLIGHT_MOUSE 1001
#define SET_BTN_EVENT_MOUSE 1002
#define SET_ANY_EVENT_MOUSE 1003
and 9 is the shortest.
Mouse-mode is turned on by many applications. If one exits without turning it off, that produces the odd characters which you saw. ncurses applications turn mouse-mode off in endwin, which all well-behaved curses application call. Other applications may not use (n)curses, or may forget to call endwin.
ncurses applications check if xterm-mouse mode is available by testing for the kmous capability (which is part of the screen terminal description). That has been the standard way to test for the feature since 1999, so it is unlikely that an application turned mouse mode on accidentally. Rather, it indicates an application that forgot to do its job.
There is, by the way, no screen.xterm entry in Debian's ncurses-term package (keeping it is more helpful than removing it). Here is a list of all of the screen-related entries in that package. Most are used for fixing discrepancies in screen behavior for various terminals:
/usr/share/terminfo/s/screen.konsole
/usr/share/terminfo/s/screen-16color-bce
/usr/share/terminfo/s/screen-16color
/usr/share/terminfo/s/screen3
/usr/share/terminfo/s/screen.mrxvt
/usr/share/terminfo/s/screen-bce.Eterm
/usr/share/terminfo/s/screen-bce.gnome
/usr/share/terminfo/s/screen.xterm-xfree86
/usr/share/terminfo/s/screen-bce.konsole
/usr/share/terminfo/s/screen-bce.mlterm
/usr/share/terminfo/s/screen-256color-s
/usr/share/terminfo/s/screen-bce.mrxvt
/usr/share/terminfo/s/screen-bce.rxvt
/usr/share/terminfo/s/screen.linux
/usr/share/terminfo/s/screen.vte
/usr/share/terminfo/s/screen-bce.xterm-new
/usr/share/terminfo/s/screen.teraterm
/usr/share/terminfo/s/screen-16color-bce-s
/usr/share/terminfo/s/screen.xterm-r6
/usr/share/terminfo/s/screen+fkeys
/usr/share/terminfo/s/screen-256color-bce-s
/usr/share/terminfo/s/screen.mlterm
/usr/share/terminfo/s/screen-16color-s
/usr/share/terminfo/s/screen-bce.linux
/usr/share/terminfo/s/screen.gnome
/usr/share/terminfo/s/screen.rxvt
/usr/share/terminfo/s/screen2
/usr/share/terminfo/s/screen.Eterm
/usr/share/terminfo/s/screen.xterm-new