What does it mean when a dove flies into your window then flies away?

We have collared doves fly into our Windows regularly. As far as we can tell. when they get very hungry, and can't find food, the fly into our Windows asking us to put food our for them. After we feed them there are no more birds hitting our Windows for a week or two. Then the cycle repeats at varying intervals. We have been told that they fly into our Windows because they see the reflection of trees in them, and they think that they are flying into trees. However, a couple of days ago, a collared dove flew into my window, then it flew off with a companion into a nearby tree, where both birds appeared to be watching to see what we would do. I fed them, and as soon as I had closed my door going inside, these two swooped down to feed what I had put out. Then around another 12 collared doves arrived and fed from our feeders. (Just one thing. When the doves hit our Windows, now it is with much less force than it used to be. When it first happened we had the outline of a dove in flight left on our window. Now they don't seem to leave any sign, and they don't appear to harm themselves. Has anyone else with the same problem solved it by this or some other way?.