Banana plugs/speaker out terminals on the back of your A/V receiver are high-powered outputs! The output from the receiver is carrying a hefty power load that runs the speakers at the other end of those wires.
The reason you got a dinky little splitter or connector, is that you only need line level connections from the receiver to the wireless speakers. You most definitely do NOT want to hook your speaker terminals up to the wireless transmitter as it will possibly damage both the transmitter and the A/V receiver.
You want to use the line level audio outputs or headphone outputs of your A/V receiver. More likely, the system has been dumbed down, so it is expected that you will just hook your CD player or cable box line level outputs (RCA type) directly to the wireless transmitter so you can enjoy audio wherever you take the speakers.
Wireless speakers, in my opinion, are a very bad option because you still must power them which requires a power cord or batteries and I can't imagine they would be immune from interference.