The family said in a statement that support from police, local authorities and specialists has been ‘beyond anything anyone could imagine’ after the incident at Carlton Cemetery earlier this month.
The cemetery was closed to the public with tents and police cars blocking its entrance - with the closure initially thought to be due to criminal damage before the Chronicle had it confirmed a grave had been disturbed.
The woman was reburied on Friday and flowers laid on her grave and neighbouring plots which were affected as a gesture of further respect.
In a statement, the family - who asked for privacy - said: "The family would like to thank each and every person that has been involved in this horrific case, for the work that has been necessary and for the work that needs to continue.
"The support we have received and the respect for us and our loved ones that have been disturbed has been beyond anything anyone could imagine.
"There are not many angels in this world but each and every person that has been involved are just that - angels.
"They have gone above and beyond their duty. As a family we have so much respect for them and they should be recognised for their work.
"The family now request privacy to grieve for our loved ones."
Detective chief inspector Andrea Bowell, senior investigating officer, said: "The family connected to this grave has been kept regularly updated on the work we have been carrying out.
“It has been an extremely sad and distressing time for them and I would like to thank them for their support and understanding while we carried out our enquiries.
“They have my sincere condolences.
"I would also like to thank members of the wider community for their patience - I know people have been unable to visit their loved ones while we have been on-site and I am grateful for your understanding."
The investigation into the matter remains ongoing.
A police spokesperson added that anyone who saw any unexplained or unusual activity at the cemetery in the time leading up to May 2 is asked to contact the police by calling 101, quoting incident number 559 of May 2.
Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website Crimestoppers-uk.org or by calling their UK Contact Centre on 0800 555 111.