On login, something in the remote shell is initializing your terminal (possibly even the ssh command itself, though that would be a misfeature). The ^[[A is a normal-mode and ^[OA an application-mode (see summary in XTerm Control Sequences), and applications such as screen which initialize the terminal for full-screen operations typically use the terminal initialization capabilities in the terminal description. mintty has its own terminal description, but sets TERM to xterm. So you're getting xterm's initialization string (see xterm-basic), probably smkx:
smkx=\E[?1h\E=
which is two settings:
If this is just a case of an application setting something and not resetting it (using the same terminal description), you could follow up by
tput rmkx
(removing that mode). Doing that inside of screen or tmux would confuse the screen/tmux program; doing it inside of some other program also might not be good...