There is no way to configure that but it seems like it might be useful in some situations. You could talk to Cisco and ask for the enhancement in future releases. In the meantime, the end call recipient will be the only one who can park the call.
It is not possible to call park from web attendant , but it has been already put in wish list for the new release.
Getting Started
Find answers to your questions by entering keywords or phrases in the Search bar above. New here? Use these resources to familiarize yourself with the community: