To delete your HomeExchange account, please click on the Profile in the upper right hand corner and from the drop down menu choose My Settings.
On the resulting page, scroll down and you will see an option to Delete your account, Click on it and follow the steps.
Do note that once the account is deleted, you will no longer have any access to it. Should you decide to comeback to HomeExchange, you will need to start all over again.
For now, unfortunately you cannot delete your account on the HomeExchange App .