At the moment it is not possible to delete conversations from your inbox.
This is a feature we hope to implement at some point this year. (The reason it hasn't been implemented yet is that it opens additional questions about whether conversations which are deleted should result in blocking that member from any further communications with you, and how other parts of the site should behave in that case.)
If you find you are receiving persistent unwanted communications from another member, just contact the Stitch team and we can remove them from your list. If you are not receiving messages from them you'll find they drift to the bottom of your inbox over time and can be safely ignored.