I wish you had called me with this one.
Since you already answered the door, it’s a little late for “Don’t open the door,” but not answering the door is a reasonable choice if you have no intention of engaging with the mission.
There are a couple of things I should explain about who they are and what they are doing out there. Typically, in our neighborhood they are Mormons or other Christians who are culturally motivated to recruit people into their church. I’ve never encountered non-Christians going door-to-door, but there’s no reason it couldn’t happen sometime.
Proselytizing missionaries are a lot more likely to be active online rather than hitting the pavement now, because that is so much more efficient. If they find an interested person, they can follow up face to face when they are in the area instead of wearing out their shoes looking for the conversation.
Just this morning I stumbled on a twitter account that was something like Koran4U and it certainly looked exactly like e-missionary work in progress.
Most of these folks are young and earnest and probably very tired. I would be inclined to give them a bottle of water and a wave.
Whatever their calling, they are trying to help you, which is very nice. They are also trying to help you in the most condescending way possible, which is actually my job.
Since they believe they understand something that you don’t and they would like to plant some ideas in your brain garden, you might consider trying to convert them to your way of thinking. Try if you like, but I have to warn you that has happened less than one time ever.
Really, just treat it like any “stranger-at-the-door” scenario. If your instinctual feeling is that they are trouble, go with that. If you prefer to take their flyer and offer to pray for them, that’s fine too.
Not opening the door is simpler.
But they are already inside the house!
Do not feed them. Just ask them to take you off their list and then ask them to leave.