You can get rid of notes shared to you by someone else via a chat, i have just worked out the steps required to do it.
***This requires rebuilding your Database we do this by renaming our old one as we still have it just in-case***
*** Before doing any of the steps perform a Sync to backup your current notes ***
Steps are as follows:
1. Delete the Work chat that contains the shared note
2. Rename the Database that contains your notes
3. Sign back into your account and download your notes
Step 1. Go to "View" then go to "Work Chat" and in the list should be the Chats, delete the chat that the note was shared from
Step 2. Go to "Tools" then to go "Options" under "General" scroll down and look at "Evernote local files" and view the file path
Go to the location in Windows and open the "Databases" folder and you should see your Database file the file will be named "yourevernoteaccountname.exb"
Close down Ever Note and rename the file and change .exb to .old if it does not let you, you need to either go into task manager and kill the Evernote process or restart your Machine. Renaming the Database extension to .old allows you to retain a backup of your notes just incase. The image below is a before and after for the one file and how the name should look.
Step 3. Open Evernote, you will get a prompt asking for your password, click cancel and then go to "File" and "Add another user..." Sign into your account and perform a sync, you should download your notes and the shared note should now be gone.
Check and ensure you have all your notes, if you do go back to the file location in Windows and delete the database file you named to .old