How can I get rid of this distortion?
You have dead band and that in itself is a desirable thing because it prevents any two MOSFETs on the same half of the H bridge conducting together and momentarily shorting the H bridge supply out (bad news and also known as shoot-through). But, it looks to me that you could probably reduce the anti-shoot-through delay and carry a little more energy to your load.

The slight glitch in rise and fall time is not a big deal and is likely caused by some driver resistance in the line that feeds each gate. Basically, as the MOSFET switches polarity an opposing voltage forces its way through the parasitic capacitance between gate and source and, momentarily halts the gate drive process. Result: you get a little glitch. It’s common enough and is probably not a cause for concern.