Yes, it's very easy to delete messages and conversations from your Inbox.
Once you have read the latest message in a conversation, a small context menu button represented by three dots will be shown on the right hand side of the conversation, as shown in the picture below.
Click this button to open a menu with two options:
- Archive conversation, and
- Block this member
Select Archive conversation to remove the conversation from your Inbox. Note that this doesn't prevent the other member from contacting you in the future. If they send you a new message, the conversation will be restored to your Inbox.
If you don't want to receive messages from the other member ever again, select Block this member. The conversation will be removed and that member will never be able to contact you again (unless you initiate a new conversation with them by clicking "Send Message" when viewing their profile).