Send them a cheque. They choose not to account for the possibility of people taking advantage of their good nature. You should give them the option of accepting payment.
The BBC aren't allowed to serve customers outside of the UK even if they wanted to due to the licensing agreements they have with content owners. NBC is the exclusive broadcaster in the United States. Anyone offering the Olympics to US viewers is in breach of their licensing agreement.
While you wouldn't be able to get them to accept direct payment for this service (since they aren't allowed to sell it to Americans), you could choose to donate to one of the other programs they run that accepts donations, such as this one: https://secure.thebiggive.org.uk/donate/donate.php?charity_i...
