Diagnosis
The rear grease channel is clogged where it meets the trap hole, causing grease to back up and spill over the sides of the trap cup. It's not about the cup being full; it's about the flow path being blocked.
How to Fix It
Let the griddle cool completely. Remove the grease trap cup. Use a putty knife or Blackstone scraper to clear the channel that runs along the back edge of the cooktop, pushing any solidified gunk toward the drain hole. Then, check the drain hole itself—poke a stick or pipe cleaner through it from the top to clear any blockage. Hot water and a little degreaser down the channel can help melt stubborn fat.
If That Didn't Work
Check that the griddle is perfectly level side-to-side. If it's tilted even slightly, grease will flow to one side and miss the channel entirely, running down the front or back lip instead of toward the trap. Use a level on the cook surface and adjust the wheels/legs.
Heads Up
Don't pour liquid grease down the drain if you wash the cup indoors—it'll clog your home plumbing. Let it solidify in the cup and throw it in the trash. Also, lining the cup with aluminum foil makes cleanup stupidly easy.