(gnu) screen defscrollback memory hog
Screen configuration variable defscrollback controls the length of scrollback for all newly created windows ("def" for default i imagine).
Take care not to set this value too large as screen seems to maintain scrollback entirely in ram. I found out the hard way after setting defscrollback 1000000 which made screen consume over 300MB ram out of maximum 512MB on my VPS.
If you really need to have so much backscroll, consider using screen's logging to file functionality.
excerpt from "man screen":
-L tells screen to turn on automatic output logging for the windows.
DEFAULT KEY BINDINGS
C-a H (log) Begins/ends logging of the current window to the file "screenlog.n".