In Order of the Phoenix Kingsley, Tonks, Moody, Lupin, and Sirius break into the Ministry to save Team DA. Did Voldemort know Kingsley, Tonks and Mad-eye were in the Order or were they just seen as Aurors?
I believe the Dark Lord knew about Order of the Phoenix and its members at that time.
Dumbledore summarized Severus Snape's job in that words:
Do not think that I underestimate the constant danger in which you place yourself, Severus. To give Voldemort what appears to be valuable information while withholding the essentials is a job I would entrust to nobody but you.
Dumbledore openly admitted to stand against "reborn" Dark Lord and it was very likely he would engage old members of the Order and recruit new supporters. Snape as a double agent must have told the Dark Lord some details about the Order.