You can delete a conversation on Session, including all messages and attachments. This will not delete the conversation for the other person's device. The person you are talking to won't be notified if you delete your conversation with them. Deleting a conversation is not the same as deleting a contact.
Here's how to delete a conversation:
iOS
From your list of conversations, swipe left on the conversation with the contact you want to delete. 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 Conversation".
Android
From your list of conversations, press and hold on the profile picture of the conversation 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 Conversation".
Alternatively, long press on the conversation and select "Delete Conversation".
Desktop
From your list of conversations, right-click on the contact you want to delete. Click "Delete Conversation".