Based on the comments, you've indicated the transmit unit works fine connected directly to the camera.
It could be that the receiver is defective. Before sending it back, however, I'd try setting a different channel on the transmitter and receiver.
Be sure you have the transmitter and receiver set to the same "channel." Both are shipped set to the default "no channel" setting and the channel indicators on both units will will display [--] (two dashes minus the brackets). If a channel is set, it will display as a two digit number such as  or  (minus the brackets).
Apparently the transmissions have digital authentication so that more than one TW-282 set of may be used in the same area without interfering with one another. From the description at amazon: "The remote control can be set to any one of the 99 channels in order to avoid any interference from any other photographers that may be working with the same remote control around you."
From page 16 of the user manual, it states that [--] is the default channel setting on the receiver. It also says that if [--] is left as the channel setting on the remote, any TW-282 transmitter operating on any of the channels can control the receiver. That might also make it possible that any other 2.4GHz transmissions in the area may also constantly trigger the remote. Many wireless devices us the microwave 2.4GHz band. Microwave ovens may also interfere with the 2.4GHz band if they are in close proximity.
Before sending the receiver back as defective, try setting the transmitter and receiver to one of the 99 available encoded channels rather than the default [--]. You might need to try several different ones to find one that isn't affected by interference in the location you are at.