It could be as I posted something to do with the TLM103 internal regulator circuit.
I have a 103 that is on loan so if I get it back I will take some measurements and trace the circuit. Without a microphone and phantom supply schematics it is harder to figure out what you are hearing.
P48 has two 6.8K (hopefully well matched resistors)
One side of the resistors goes to 48VDC
the other sides go to pins 2 and 3
So with a 3mA current consumption
https://en-de.neumann.com/tlm-103#technical-data
The following is with no added resistor in a RC filter after the 48VDC supply(see Walrus's post)
1.5mA x 6.8k = 10.2VDC (1/2 of the current to pins 2 and 3)
48VDC - 10.2 =37.8VDC at pins 2 and 3
DC power = voltage x current
37.8VDC x 3mA = .1134watts
If you change the 6.8ks to 2.2K. The current consumption will go up with lower phantom resistor values because there is less voltage drop across the phantom resistors and a higher DC pin 2 and 3 voltage
So the higher power will most likely be dissipated in the microphone regulator circuit.
Some microphones use the power from pins 2 and 3 to power a voltage regulator set lower than the voltage at pins 2 and 3 with the microphone powered up. Sometimes this regulated voltage powers a DC to DC converter for the capsule voltage.
The extra power is "burned up" in the regulator circuit.
Maybe the power supply noise goes up with more dissipation due to higher heat or current causing changes in the microphone power supply noise.
Or maybe a cap(s) voltage rating is being exceeded with the higher voltage at pins 2 and 3
Have you done this test from the shure web site
http://www.shure.com/americas/support/find-an-answer/how-to-test-phantom-power-voltage-and-current
Maybe the phantom supply that you compared the P48H supply to can not supply enough current to the TLM103.
It could be something like a too high a value R in the RC filter in the phantom supply like Walrus posted. This resistor is in series with the phantom resistors. You can figure this resistor value out with the current and voltage measured at pins 2 and 3 with different resistor loading and using ohms law.
I would not like anything greater than 100 ohms as an extra series resistance in the P48