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On any Tek scopes I have the calibration signal is a square wave.
Bypass the probe and connect a Y input to the calibration signal and see if the waveform changes. This will eliminate the probe as a cause. Check all Y channels. My 7603 has 4.0, 0.4, 0.04 outputs.
Service from Tektronix is very expensive.
The scope might be fine except for the calibrator. I doubt that the calibrator was designed as a sawtooth generator. One of the uses for the calibrator is to do high frequency compensation of the probe. The square corner of a square wave is best for this.
To check the basic operation of the scope there are other procedures you can use.