Shell – How to set Cols and Lines for a Subprocess

I have a script that runs a series of scripts numbered 001,002,003,004… etc down to 041 right now, will be more in the future – and these scripts them selves use some cursor control to print a progress bar and other status information and get the width and height of the terminal from tput cols and tput lines respectively.

Without rewriting the sub-scripts, I would like to reserve one line at the bottom for overall status information for the outer script. I was curious if there was a way to set what tput replies for lines and cols.

There must be a way because tmux achieves it. I was thinking there may be an environmental variable but the only change I can see that tmux makes when running env is setting the $TERM to screen.

Any help would be greatly appreciated