You can delete a contact on Session. This will also delete your conversation, including all messages and attachments. It will not delete your contact or your conversation from your contact's devices.
Future messages from this contact will appear as a message request. The other user will not be notified if you delete their contact, and they won't know that their messages to you are taking the form of a message request.
If you delete a contact, it will be deleted across all synced devices.
Here's how:
iOS
Search for the conversation, swipe left, and select "Delete Contact".
Open conversation with the contact you want to delete. Tap the display picture icon in the top-right hand corner to open the conversation settings. Scroll down and select "Delete Contact".
Android
From your list of conversations, press and hold on the profile picture of the contact you want to remove. Tap "Delete".
Open conversation with the contact you want to delete. Tap the display picture icon in the top-right hand corner to open the conversation settings. Scroll down and select "Delete Contact".
Alternatively, long press on the conversation and select "Delete Contact". Or search for the conversation, tap the conversation, and select "Delete Contact" on the pop-up menu.