After the contract with the Great Devils was completed, Hecate returned to Gehenna shortly after to deliver the recording crystal to the other Great Devils.
Although the recording crystal wasn't necessary for the Great Devils to find out about Vaan's agreement to join their circle of Great Devils, it still contained the full details of the process.
Just seeing Vaan's name in their shared contract wasn't enough to satisfy them.
After all, Vaan's existence was too special to be taken lightly; he was a big variable capable of changing the trajectory of their lives. Thus, reviewing the recorded proof was absolutely necessary.
Nevertheless, when the Great Devils sensed the changes to the shared contract within their seas of consciousness, they immediately checked it.
Before they could feel assured with the addition of Vaan's name to the list, they quickly noticed the special clause that came with it.
Thanatos: "…"
Mephistopheles: "The… fuck?"