Winehouse and her hubby had said that they left for London to fetch a guitar.
The couple's constant fights were spoiling the centre's ambience and a source said that though Winehouse would be welcomed back, Fielder-Civil might not get a similar reception.
The source added that everyone is worried that the two will get back to their druggy habits.
"It is supposed to be a peaceful backdrop to help people deal with their problems. But Amy and Blake kept rowing and spoiling the ambience,' the Sun quoted the source, as saying.
"While Amy would be welcomed back with open arms, I'm not sure they'd say the same for Blake."
"Everyone is really worried that if they are let loose in London again they'll just go straight back to their old druggy habits."
The source also said that Fielder-Civil's behaviour shows why the soul star's family wants her to seek 'help without him'.
"He upset people in The Causeway with his behaviour. It was the same when she was in hospital. He really upset the staff and wasn't very welcome there either," the source added.
"They spent half their time arguing rather than concentrating on the job in hand. Of course it must be stressful being with your partner while trying to sort out something so personal and difficult."
"But this just shows why the family are so desperate for her to get help without him."
Winehouse and her hubby checked into rehab after a massive showdown involving the couple's families.