My name is ***** ***** I am a NSW Solicitor. Thank you for your question, and will do my best to assist you with your question. Please understand this is not legal advise Please understand this is not legal advise but a guide to assist you.
It appears that they agreed the cat was yours and you have the right to it.
If they want to take it now they are not the legal owners.
By allowing the cat to live with you, it can be interpreted that they have given up all rights to the cat.
You do not have to allow the cat to go anywhere and if they want to take it they would have to get a court order.
They have agreed to allow the cart to live with you and since that date you have provided and looked after the cat that is enough evidence to show that they have given up the right to the cat.
I hope this makes sense and is of assistance. If there is nothing further
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