Hi Kathryn,
Not all machines are designed to drop their feed dogs. Some use some sort of covering device for the feed dogs. Some have nothing. I have no idea of whether it will hurt your machine if you remove the feed dogs.
What model of machine do you have? It should be on front of the manual, if not on the machine. Any of the technical people will need to know that.
Hopefully, someone will have an answer for you.
bkay