Prepare a medium-hot grill fire (be sure the grill grate has been scrubbed clean with a wire brush).
Cut the half lime into four wedges and set aside. Finely grate the zest from the whole lime. Cut the zested lime in half and squeeze the juice from one half into a small bowl (save the other half for another use). In a medium bowl, combine 1 tsp. of the lime juice with the lime zest, mayonnaise, wasabi paste, ginger, and 1/4 tsp. salt. Stir to combine. Taste and add more wasabi paste if you’d like a zippier flavor.
Run your finger along each salmon fillet to feel for tiny bones; use tweezers or needlenose pliers to pull out any that you find. Season the fillets lightly with salt and pepper. Spoon about 2 Tbs. of the mayonnaise mixture onto the salmon fillets and refrigerate the rest. With your hands, spread the mayonnaise in a thin layer over all sides of the fillets.
When the grill is ready, oil the grill grate using tongs and a paper towel dipped in oil. Grill the salmon until crisp and slightly charred on one side, about 4 minutes. Turn and continue to grill until the salmon is just cooked through, another 3 to 6 minutes. Serve the salmon topped with a dollop of the mayonnaise and a lime wedge on the side. Pass the remaining mayonnaise at the table.