In order to delete texas holdem poker buddies (not friends on facebook) on zynga poker you must follow the following steps.

1) click on profile inside zynga poker lobby, this way you will see you profile.

2) Next to your name there is a button [Show Buddies] Click it.

3) Then select a friend and mouse over to who you are willing to delete, click him and then click ok.

Thats it you are no longer friends at zynga poker. Remeber you can't delete this way a facebook friend.