Using a line choke (inductor) that was designed for 50 Hertz on a 60 Hertz power system would appear to be an error/omission on the part of the designer/engineer but it can work satisfactorily if it is applied correctly and operated within its ratings: volts/hertz, voltage, current, harmonics, volt-second balance, temperature, etc.
The high levels of noise can be due to many factors. The most likely are harmonic currents produced by the drive, excessive saturation if it uses an iron core, loose or shorted windings, loose core iron, loose housing or bracing, etc.
I came across a 4.16 kV tuning inductor used in a harmonic filter once that was so loud than you had to plug your ears to stand next to it and you could not have a conversation while standing in the room. We de-energized it to find that one of the phases had developed a fault and burned open producing a single phase condition. The inductor continued to be operated for years in this condition and the operators thought it was normal because it always sounded the same - loud enough to make your ears bleed. The windings and core iron were all loose and flopping around caused by years of excessive vibration.
Removing the line inductor could cause the drive to function differently than designed and might result in damage to the switching semiconductors used in the rectifier and inverter power stages. You should consult with the manufacturer.
If the motor drive power converter is configured as a boost converter or active front end (AFE), the line inductor on the AC side of the rectifier serves three purposes: (1) to store and release energy to the load through volt-second balance; (2) to reduce the DC current ripple; and (3) to reduce the current harmonics which flow back into the 50Hz/60Hz AC system.
It is a good idea to include an audible noise maximum limit when specifying line inductors. You might check the original specification that was used to procure the drive to see if a noise limit was specified. If it was not, the supplier was free to design with the objective of minimizing costs in the selection of components, ratings and loadings.
You might also consider questioning the 50 Hz nameplate being used in a 60 Hz system and ask them to justify their design calculations to you. If they reveal that the inductor is operating within the design limits for the 60 Hz application, the issue might be poor quality in workmanship and manufacturing. Replacing the inductor with one that is designed to operate at a reduced noise level may prove to be the solution. In the meantime, you will have to wear good hearing protection.