Using your neighbor's grill for your party without their explicit permission would generally be considered rude and invasive. Borrowing or using someone else's property without their consent is not appropriate behavior, even if you intend to clean it afterward.
Instead, it's best to ask your neighbor if they would be okay with you using their grill for your party. Respect their decision, whether it's a yes or a no. If they agree, be sure to handle their property with care, and definitely clean it thoroughly afterward as promised.
Good communication and respect for boundaries are essential in maintaining a harmonious relationship with your neighbors. If you find yourself in need of a grill for your party and your neighbor isn't available, consider using your own grill, renting one, or asking another friend or family member if you can borrow theirs.