It is useful to know the first mode from a Modal analysis, which is 33683 Hz when the part is in contact.

That helps you to calculate a time increment and damping. The period for 33683 Hz is about 3e-5 s, which is for a full cycle. You want at least 20 time points over that period, so 1.5e-6 is a good Initial and Maximum Time Increment for Transient Structural. I used the values below.

Use a Damping by Frequency input of 2% at this frequency.

Put a Directional Deformation and a Directional Velocity plot in the X direction on a corner vertex of the moving part, distant from the contact surface. Here we see the damping working on the part.

You can see that at t=1.6e-5 s the bounce is finished and the contact starts to separate, moving away at about 181 mm/s. The other end of the slot is 2 mm away. This is where the free fall began and gave the 198 mm/s initial velocity at impact. Since the departing velocity from the impact is only 181 mm/s due to damping and frictional contact losses, the part would not reach a 2 mm displacement if Gravity in the -X direction was included in the simulation. Gravity was not in the model, but including it makes an insignificant change during the 1.6e-5 s of the impact event.

If there was no friction in the support of the moving part, it would make a second impact at 181 mm/s instead of 198 mm/s for the first impact. In reality, there is likely to be friction both going up and falling down. This is a 2D simulation so there is no motion out of plane. In a 3D simulation the bounce would not travel perfectly along the X axis, but would rotate and go off at some small angle so the second impact would not be perfectly level with the surface, dissapiting more energy than the first impact.