There's another method if you want to avoid removing the tank lid: Fill a bucket with water. Lift the toilet seat and lid. Dump the water into the bowl with one pour. Pouring slowly will only fill the bowl, so pour with as much force as possible to create a strong flush. Repeat until the bowl is clean of any residue.
During the interruption in service you can flush your toilet manually with a. Repeat dumping in another gallon of water if necessary to clean the bowl of any .