Carter Single BBS Issues

Yep, they sent you the wrong part. That choke pull-off is for a Holley 1920, not a Carter BBS. They probably sent a '62-'65 choke thermostat which is almost but not quite the same as the '66-'69 item you need (Carter BBS or Holley 1920 thermostat doesn't matter; they're fit/function interchangeable, but you do have to have the right pull-off for the carburetor at hand.)