Belfast Trust has apologised to the Jones family and said it was working with the company “so that this does not happen again”.
However, on Friday the RQIA said it had “directed Liaison Care to cease and desist from its activities in Northern Ireland with immediate effect”.
“In recent days, RQIA has become aware, including through contact from concerned families, of the commissioning by HSC Trusts of Liaison Care, a company which RQIA understands is based in England, to carry out activities in relation to services being provided to people in Trust care,” it said.
Liaison Care is not currently registered with the authority, it said.
“RQIA also has concerns having learned that a number of individuals and their families have been contacted by the company, and is aware of the distress this has caused.
“This forms an important part of RQIA’s ongoing enquiries into the nature of the work being undertaken, including in relation to the care and treatment of individuals subject to mental health legislation,” it said.
RQIA added that issuing directions to organisations for them to cease operating is a necessary part of its statutory regulatory role and that it typically issues a small number each year.
It also said it will be engaging with Liaison Care.
BBC News NI has approached Liaison Care for a response.