I am under the impression that you have an API/service that handles sending/receiving messages on both ends of the chat. So, my suggestion is to add an extra parameter to your message element class that can toggle the status (thus the UI - showing 'This message has been deleted' or hiding the message altogether) of the message based on whether sender has deleted the message.
Each message would have a unique identifier, and based on this you can send a request to your server to update the status of the selected message on the receiver end.
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