A "rush fee" is an extra charge or fee that is added to the cost of a service or product when a customer requests it to be completed more quickly than usual. Full definition
The most basic ways to save on shipping is to recycle all packing materials you receive and plan ahead to avoid rush fees. (creditdonkey.com)
The rate structure for 2018 will include rush fees (starting with $ 100 above basic fee) as determined by me (usual turnaround is about two to three weeks). (Emsflynn.com)