putty and gnu screen scroll back with mouse

Summary: add the line to your .screenrc file:

termcapinfo xterm ti@:te@

Reference ( Putty FAQ )

PuTTY's terminal emulator has always had the policy that when the ‘alternate screen’ is in use, nothing is added to the scrollback. This is because the usual sorts of programs which use the alternate screen are things like text editors, which tend to scroll back and forth in the same document a lot; so (a) they would fill up the scrollback with a large amount of unhelpfully disordered text, and (b) they contain their own method for the user to scroll back to the bit they were interested in. We have generally found this policy to do the Right Thing in almost all situations.
Unfortunately, screen is one exception: it uses the alternate screen, but it's still usually helpful to have PuTTY's scrollback continue working. The simplest solution is to go to the Features control panel and tick ‘Disable switching to alternate terminal screen’. (See section 4.6.4 for more details.) Alternatively, you can tell screen itself not to use the alternate screen: the screen FAQ suggests adding the line ‘termcapinfo xterm ti@:te@’ to your .screenrc file.