Is one sinful for not killing a gecko due to inability to do so, and is its droppings that touch the mosque carpet excused without washing the spot, and does this fall under the principle of "hardship brings ease" or is it considered among what has no flowing blood?

The command to kill geckos is religiously established and is linked to one's ability. If a person is unable to do so, there is no blame upon him. It has also been commanded to purify and clean mosques. If killing geckos is not possible, the mosque should be protected from them by repairing cracks and sealing entrances. A gecko has flowing blood, and its droppings are impure. They must be swept if they are dry and visible; simply removing them by sweeping is sufficient. If a small amount remains, there is no harm. However, if the droppings are wet, they would have affected the carpets, in which case they must be washed with water until the impurity is removed.