You can archive conversations to hide them from your Messages page. Messages will be unarchived automatically if the other side sends you a new message.

To archive a conversation with someone, go to your Messages page and use the sidebar option shown in the bottom right (on mobile, this can be accessed through the 3 dots button at the top of the conversation):

You'll then be able to view any archived conversations by clicking the "See Archived" option shown - this is located at the bottom of the list of conversations you have on the left-hand side.

From there, you can see when you've archived the messages and can also unarchive them to read the chat and reply again.
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