If you don't know what the problem is, you can't find a solution. You first need to diagnose if it is the laser giving the problem, or the 4-20mA transmission, or the Motion controller. Before that you need to know if the diagnostic tools you have can see the problem. You probably have a multimeter, you might have an oscilloscope. Using a multimeter you need to measure the 4-20mA that is in the loop, the obvious way is to set the meter to a mA scale and insert it in to the loop. Can you see the variations? If you can then the multimeter is the tool to use, if you can't then you will have to go to an oscilloscope, or the controller has issues.
Once you have a diagnostic tool you can break the problem down. First remove the loop and controller from the problem and concentrate on the laser. You need to know if it has an active or passive output so you can decide if you need to power the short test loop. The simplest way is to connect a variable resistor across the output, the laser documentation should give you a minimum and maximum loop resistance if it supplies the loop power. If you get current flowing then you know that it is an active output. If you don't then you will need a power supply to power the loop. Can you see the variations in the short loop, if you can then it is a laser problem and you will have to look at the choice of type and make of sensor.
If the variations have gone then you need to look at the 4-20mA loop. The most common problem is a ground loop where different parts of the circuit have different 0V levels, you can solve it by tying 0Vs together or by fitting loop isolators. Another problem is too great or too small loop resistance, check the laser documentation. Next if there are two things trying to power the loop there can be issues, read the documentation for each device in the loop.
If you clear the laser sensor and the loop then you have a club with which to beat the controller suppliers.