The Bluetooth transmitter they sold you will only work if the TV has a headphone or analog audio output. The one linked to above will work with an optical audio output too. That's the most common type of audio output on TVs. You will need a toslink cable to connect it to the TV.
Then you need any bluetooth wireless speaker. Why did the sell you wired speakers? Who knows.
You want a speaker that doesn't need to be loud to be clear so if you can audition them turn the volume down and listen for how well you can understand dialogue.
Check the TV manual on how to use the audio output. You may need to turn it on, turn the TV speakers off and change the audio output to PCM stereo to get it working.