I believe you can just add a line like this to your ~/.screenrc:
termcapinfo xterm* ti@:te@
Where “xterm*” is a glob match of your current TERM. To confirm it works, ^A^D to detach from your screen, then screen -d -r to reattach, then ls a few times, and try to scroll back. It works for me.
What is this magic? Well, let’s consult the manual pages.
screen(1) says:
termcapinfo term terminal-tweaks [window-tweaks]
[..]
The first argument specifies which terminal(s) should be affected by this
definition. You can specify multiple terminal names by separating them with
`|'s. Use `*' to match all terminals and `vt*' to match all terminals that
begin with "vt".
[..]
Some examples:
termcap xterm* LP:hs@
Informs screen that all terminals that begin with `xterm' have firm
auto-margins that allow the last position on the screen to be updated (LP),
but they don't really have a status line (no 'hs' - append `@' to turn
entries off). Note that we assume `LP' for all terminal names that start
with "vt", but only if you don't specify a termcap command for that terminal.
From termcap(5):
String capabilities
[..]
te End program that uses cursor motion
ti Begin program that uses cursor motion