The term third wheel is a corruption of fifth wheel, which refers to someone who deters the socialization of a couple, perhaps when being invited out of pity or through a feeling of duty.

Third Wheel
Third Wheel
Third Wheel
Hypoxia: the third wheel between nerve and muscle.
Third wheel & pinion disengaging structure and timepiece possessing the same
The third wheel: the impact of Twitter use on relationship infidelity and divorce
Electronic health records: an awkward third wheel.
Hypoxia the third wheel between nerve and muscle Neurological Research Vol 30, No 2
‘I felt like a third wheel’: Fathers’ stories of exclusion from the ‘parenting team’
A gluconeogenic tryst in the nucleus, with ER stress as the third wheel.