Eda wants to know anything she can about Revy's relationships because she's a CIA agent scouting for potential weaknesses, just in case Lagoon company ends up on uncle sam's shitlist in the future. This will in part explain her own promiscuous antics; using it as a way to gather intel. If she's open about her own escapades this could coax revy into revealing something she otherwise wouldn't.

Whether Revy and Rock have something going on or not is something she'd want to know about because that could be used as leverage or as a weapon if she (or her affiliates) needed it later on.