So.. each member can configure the notification preferences for the thanks they receive.
When you send a thanks it displays to the member who sent it on their profile page and they may of may not get a notice about this depending on the notification choices they've made.
You can check your settings here:
https://www.irv2.com/forums/profile.php?do=editoptions
To see if you have received thanks click here and scroll down.
https://www.irv2.com/forums/usercp.php
For those sending thanks - they are sent automatically by the system and even if the member who received the thanks has elected to get a a PM, the sent item will not display in the sender sent folder.