The handle attaches via clamps and bolts to the beam assemblies. Tighten the hexagon socket screws.
Locate the clamp (part 202-20) and clamp block (part 202-5). There are multiple hexagon socket screws (part 202-19, 32 total in the assembly) securing the handle set (part 202-23) to the beam assembly (part 202-401 or 202-402). Check and tighten all of them.
If tightening doesn't fix the wobble, the rubber block (part 202-4) inside the clamp may be worn or crushed. This part provides grip and dampening. Replace it if it's degraded.
For a persistent wobble, inspect the beam assemblies themselves for cracks, especially near the screw holes. A cracked beam requires replacement.
A loose handle affects control and safety. Do not use the mower until the connection is solid.