Hello to you JeffRam,
I completely understand the option for discretion being important. At this time those who have been blocked when contacting you will hear the following message, "Welcome to Verizon Wireless. The number you were trying to reach has calling restrictions which has prevented the completion of your call." However I will ensure I pass your feedback to my leadership to see if changes can be made.
For more details on Call and Message blocking please here: http://bit.ly/Qm5Yrd
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The blocked caller just hears the phone ring and after about a minute of ringing it just goes silent. I just tried it with another phone.