Looks like you are using a generic probe. Switch input mode to DC coupling and see what happens and the waveform changes or clears up. Or there might be some interference or grounding problem that is distorting the waveform. Have you tried to compensate the probe until the square wave displays properly? (flat tops and bottoms). Are you sure the probe is working correctly? (tested in another scope). Also do you get the exact same waveform display if you use CH2 input instead?
Another possibility, since you are at 50nS time base, and the calibration test frequency that the scope outputs at this setting might be higher than your generic probe can handle. Can't remember what frequency is used at this setting, but worth a try to go to a lower setting, like 1uS and see if the waveform clears up
BTW for a probe calibration setup you don't need to connect the grounding clip of the probe to one of the BNC shells, as the probe should already be properly grounded at the CH1 input that you are using. Just in case try disconnecting the ground clip from the BNC shell and see if the waveform changes. It should not.
Also keep in mind that if you are using a 1X/10X switchable probe you should set it for 1X to make sure amplitude readings are correct on screen. If its a 10X make sure to do the calculation in your head, as generic probes without the sensing pin will not properly adjust the amplitude scale on the scope when switched to 10X.
Ideally at some point you should get a proper Tektronix scope probe like the P6037 (or better yet a pair of probes) which will allow you to take fully advantage of this very fine scope you have.
Also since this is a '67B, be careful with the screen intensity setting, keep it on a not too bright (normal) level, as otherwise you would be straining and unnecessarily wearing out the super sensitive screen, which is the main feature of this scope over a regular '65B.