If the seed fell into your lawn (grassy area) I would think you could use a shop vac and get up what seed you can, and I'd also rake reallly well.
We quit feeding the birds several years ago - they made a huge mess in the yard and I and a lot of odd weeds sprouting...I don't think our dog ever ate the seed, but that would have been enough for me to quit feeding them as well.
Our neighbor has a feeder in the front yard and it does cause some problems...lots of birds flying around and we have had a few birds fly into the garage...I am terrified of birds....yes I know they won't hurt me but the fear is real....we usually have the garage door down but on occasion its open for several hours....and along with the birds come squirrels.