Is this the first time you have posted anything to do with your grandchild on Facebook?
If it is, it might have been wiser to ask your son or daughter-in-law in advance.
You could e-mail your DIL and ask nicely whether you have done the wrong thing, as now you are in doubt.
If on the other hand, you normally send the entire family a birthday greeting when Facebook reminds you of a birthday, just let it go.
They may, or may not, get round to thanking you. Their generation attaches far less importance to "saying thank you nicely" than ours.