Is it permissible to donate the remaining funds from mosque construction to the needy, especially in Palestine, with the intention on behalf of its owners whom the donor does not know?

As long as you do not know the owners of the money you collected for building the mosque, you must spend it with the intention of earning reward for its owners. It is preferable that this be for building a mosque. If it is not possible to spend it on that, then it should be spent on the most needy charitable causes.