While your intention to clean the grill afterward shows consideration, it would still generally be considered rude to use your neighbor's grill without their permission, especially if they are not aware of it. Borrowing someone else's belongings, even if you plan to clean them afterward, can still be invasive and may not be appreciated by the owner.
To avoid any potential issues or misunderstandings, it's best to respect your neighbor's property and privacy. If you want to use their grill for your party, it's always a good idea to ask for their permission first. This way, you can ensure that they are comfortable with the idea, and it will help maintain a friendly and respectful relationship with your neighbor.