From their site: cancel your account by following the “Cancel Account” link at the bottom of the Account Page: https://www.transferbigfiles.com/account
Also, for paying members: to request a refund, first, cancel your account, then email us at firstname.lastname@example.org requesting a refund along with the billing information (billing first/last name, email address) you used to signup for the account.
Finally: how long are my files kept? Free Site: 5 days. Premium Accounts: You determine how long files should be kept. In other words, you may want to delete those first, if you have a premium account.