You can send a removal request to webmaster@beckett.com.
However, from their privacy policy we learn that they keep a lot of data on their servers:
"Requests for removal of your registration information does not ensure that such information will be completely removed from the Beckett system. Beckett does retain registration information as a record of all activity performed on the site. Additionally, information is retained in order to enforce the Terms of Agreement, resolve disputes and problems associated with the site."
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks: this can be found mostly in the Terms of Service/Privacy Policy; otherwise you can always contact Beckett.com and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for Beckett.com using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Beckett.com. Click the icon below to find out how.