DIAGNOSIS The nonstick coating is degrading, which happens with age, high heat, and aggressive cleaning. No, it is not safe to keep using plates where the coating is actively flaking into your food.
FIX You need to replace the grill plates. For the GR2144P 9-Serving model, the part numbers are usually something like “Plate Set, Grill & Griddle” and they are sold as a pair. You can find genuine or compatible replacements online. They slide out easily once the grill is cool—just lift up on the front edge and pull them forward.
IF THAT DIDN'T WORK If new plates seem expensive or are hard to find, your only other option is to replace the entire grill. Trying to re-season or re-coat the plates yourself isn't effective or food-safe for this type of appliance.
HEADS UP To make the next set last, never use metal utensils or abrasive scrubbers. Let the plates cool before washing, and hand-wash them instead of putting them in the dishwasher, even if they claim to be dishwasher safe. The detergent and heat accelerate coating breakdown.