backspace => ^? in remote vi under screen, all shells zsh

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I have this annoying problem -- in my local zsh and screen everything is OK.  But when I log into certain Red Hat 7.2 boxen from a window in that screen, and start vi, backspace produces ^?.  Note that *remote* shell is zsh and backspace in its command line works just fine.

 

I dug out the solution for (the local) screen -- tell it

 

bindkey ^? stuff ^H

 

That fixes the remote vi, keeps remote zsh happy, but breaks the local screen itself fscking up ^A <backspace> which no longer moves to the previous window until it eats an extra key press or something.

 

I wonder whether this is a problem which can be fixed on zsh's own bindkey level?

 

Cheers,

Alexy