A shunt capacitor might well do the trick. Certainly worth a try. It will also delay the on and off action by a bit, but if that's tolerable and it can stabilize the voltage sufficiently, then that's good enough.

OK, I did make two assumptions, first being that the buzzer is to alert a human with normal response times and second that the frequency is at least 500Hz. Then with a reasonably small capacitor , 0.1mFd, the voltage variation will not be so big. And the one electronic buzzer that I put into a piece of equipment used a CD4049 with a one-inverter oscillator, one stage phase inverter, and two groups of two inverters in parallel driving a magnetic speaker in push-pull, it would work from about 3 volts up to 15 volts, with almost 2 Vdd driving the load. Noismakers should be able to tolerate wide variations of supply voltage.

 

OK, I did make two assumptions, first being that the buzzer is to alert a human with normal response times and second that the frequency is at least 500Hz. Then with a reasonably small capacitor , 0.1mFd, the voltage variation will not be so big. And the one electronic buzzer that I put into a piece of equipment used a CD4049 with a one-inverter oscillator, one stage phase inverter, and two groups of two inverters in parallel driving a magnetic speaker in push-pull, it would work from about 3 volts up to 15 volts, with almost 2 Vdd driving the load. Noismakers should be able to tolerate wide variations of supply voltage.

Also, I would think that there would be a very good chance that a buzzer would have its own built-in decoupling capacitor, as I mentioned earlier, but you can never be too sure.

 

Also, I would think that there would be a very good chance that a buzzer would have its own built-in decoupling capacitor, as I mentioned earlier, but you can never be too sure.

If his does, it is apparently not sufficient to handle using a resistor to drop the voltage all the way from 24 V.

 

I would add another "unless" -- Unless the 15 mA isn't pretty reliable and constant. Let's say that you use a 1.3 kΩ resistor and, under some conditions, it were to draw only 14 mA then the voltage across it would be 5.8 V while if it were to draw 16 mA the voltage across it would only be 3.2 V -- and that's with only a 1 mA variation from the expected current.

I wonder if the TS has a scope? It would be easy to just look at the voltage on the buzzer.

 

Also, I would think that there would be a very good chance that a buzzer would have its own built-in decoupling capacitor, as I mentioned earlier, but you can never be too sure.

I would not presume that a device that is able to operate without an internal supply bypass cap would actually have one. Given that capacitors take up space and cost a bit, they are mostly left out of a whole lot of products. Many digital ICs in most applications should have a supply capacitor, but it is never part of the IC.
So it is wise to not trust that any device includes such a cap, unless it is clearly stated. This is especially true for noise makers.