Apple can only put a new 6s screen assembly on a phone when there is are no dings/dents/slight bends in the frame. These defects are common after drop. Quality independent repair can use professional tools to reshape the frame of your phone to properly fit a new screen.
If you take any phone to Apple for a screen replacement, they have the right to "bounce" your phone for minor frame defects and instead replace the phone at the out of warranty replacement price. My guess is that this is disclosed to you when you signed papers granting permission for the screen job.
The price for independent repair original quality 6s screens is still about $200+, so your best bet on the 6s is still probably sucking it up and getting the replacement phone at Apple. If the damage is something you can live with for a few months, the parts price on the 6s original quality screens will likely come down by $100 or so as the Chinese New Year comes to a close and production ramps up.