Not heard of one doing this with a blanket from the vet ! Most dogs don't want anything that reminds them of there :). We give a new owner something from here which has a familiar smell, such as a bit of cloth or blanket that the pup has slept on.The familar smell is very comforting and they won't be separated from it, choosing to sleep on and lie with it.. Your little bitch is finding the same.
She'll gradually grow away from this once she has settled and found her own personal bedding and has come to associate your smell, and home 'smell' , and you yourself, with happiness.
Wouldn't bother to separate her from it: quite the reverse.It's doing no harm and she's happy.(I wouldn't wash it either, unless absolutely essential. Don't want to remove that 'lovely' scent !)