Meaning of "garnish"

c. to attach (a debt)

It means to extract payment by appealing to legal authorities. In this context creditors can't get your assets if your assets exist outside the "standard" channels.

It's referring to attaching the money to a debt, sort of. It's more accurately Wage Garnishment or something similar. From Wikipedia:

Wage garnishment, the most common type of garnishment, is the process of deducting money from an employee's monetary compensation (including salary), sometimes as a result of a court order. Wage garnishments continue until the entire debt is paid or arrangements are made to pay off the debt. Garnishments can be taken for any type of debt...

The quote appears to be discussing money laundering or otherwise hiding money from legal garnishment.