This seems to be already added in ncurses distributed terminfo files, which are used for screen on most systems.

% infocmp screen|grep kmous
        khome=\E[1~, kich1=\E[2~, kmous=\E[M, knp=\E[6~, kpp=\E[5~,
% infocmp screen-256color|grep kmous
        khome=\E[1~, kich1=\E[2~, kmous=\E[M, knp=\E[6~, kpp=\E[5~,
% infocmp screen-16color|grep kmous
        khome=\E[1~, kich1=\E[2~, kmous=\E[M, knp=\E[6~, kpp=\E[5~,

Using kmous/Km.

Possibly should be a separate terminfo entry, in case advertising mouse support triggers dependency on the mouse in the app, when screen isn't actually running in a display that supports mice. Or, it could go into the primary entry, and a new alternative entry could remove the feature.

See also https://savannah.gnu.org/bugs/index.php?24075 for using kmous/Km to detect mouse support.