Lynne is with an unnamed friend. The friend tells Lynne that her parrot used to live on an oil rig. Lynne asks if his language is pretty crude when he talks. Her friend says it is not, but he does tend to gush a bit.
Lynne's friend's parrot used to live on an oil rig. This means that either her husband used to work on an oil rig, or knows someone who did who needed to get rid of a parrot, or the pet shop owner gave the parrot an elaborate back story in order to shift the parrot quickly.
On first glance it seems that Lynne and her friend are attempting to out-pun each other. Actually this is rather a normal conversation. Lynne wonders if this parrot swears, partly because she thinks that many men on an oil rig would swear a lot, but also because she is ill-educated and believes that parrots actually talk rather than mimic humans. Her first assumption would be more correct.
Her friend says that the talking is not a problem, but he does have a discharge problem. She says he gushes, which makes it a strange choice not to keep the parrot in a cage. They have taken him to the vet but all he could do was prescribe some tablets which are difficult to administer to an irate parrot. Perhaps this is why the pet shop owner was so keen to get rid of him.