MSK signal recoverd though FM Discriminator?
It is possible that the sample data has a pulse-shaping filter before the frequency modulator. That would explain the first plot.

Look at the power spectrum of the sample data and check the sidelobe levels as compared to textbook MSK and your modulator. A pulse shaping filter will reduce the sidelobe levels.

Square waves are expected in the second plot, because the data entering the modulator has no pulse shaping on it. The spectrum should be textbook MSK.