Thanks for taking the time to post in the community about this desire! We are thrilled to have you turn to this platform for answers.
I can confirm for you that currently there is NOT a way to delete the customer list. This is not something that you haven't reached a high enough subscription level, or anything along those lines to "unlock" this functionality. We simply do not allow for customer record deletion across the board in ShipStation.
Absolutely feel free to check out the article that we have about Updating Customer Records to learn more!
I hope this helps!