By design, there is some play on the Hand-E fingertips. It's the normal behavior. But sometimes, customers who use custom fingertips will notice that they are abnormally loose.
This can happen when the fingertips are longer. Basically, with custom design longer fingertips, the bit of play expected for the Hand-E is going to appear more important since the TCP is now further away from the gripper.
Here is another potential explanation: fluids such as cutting oil may have entered the top casing and may have "pushed out" or "mixed" with the Mobilith SHC1500 grease that is applied when the gripper is first assembled.
The Mobilith SHC1500 grease allows proper movement of the rack and pinion but also provides restriction and adherence for better gripping force.
Solution
The solution would be to follow the "Rack and Pinion Mechanism Cleaning", Section 6.3 of the Hand-e Instruction Manual. Link here: Robotiq Hand-e Instruction Manual
It will instruct the customer on how to disassemble, clean, regrease, and reassemble the Hand-e gripper. The issue should then resolve itself. Needless to say, make sure the customer has also tightened the screws holding the custom fingertips to the gripper racks.