Smoothing modified sine wave inverter
I would suggest that an inductor in series with the load may help.

Most times, a Modified Sine Wave inverter produces a simple square wave output with significant OFF-time.  The peak voltage matches that of a sine-wave and the off-time is increased such that the average voltage is equal to that of a sine wave.

But it's still a square (rectangular) wave.

Placing a capacitor across the load is a bad idea because the peak current will be very high.  Look at the leading edge of the waveform - it's almost vertical.

However, an inductor in series with the load may slow the edges sufficiently that the motor is "more happy" than with the plain square wave from the inverter.

Size, current rating, inductance value is "left as an exercise for the student".