Not easily. A LED is an On/Off device like a light bulb, and the Laws of Thermodynamics forbid light-bulbs that shine when the power is turned off!
So inversion needs an extra circuit, with power, that switches the LED on when the signal is off (logic Low), and off the signal is on (logic High).
Easiest to do with a logic chip like the 4049, but a transistor circuit like this should work too:

When signal is Low, transistor T1 turns off allowing T2 to be turned on by R1 and lighting the LED via R2.
When signal is High, T1 turns on, shorting R1 to ground and turning T2 off.
So the modification needs a circuit connected to a source of power. The LED shows the unit has power but isn't doing anything because it's in standby. As this isn't mission critical, the easy answer is to disconnect the LED so it never comes on!
Sorry to hear about Mrs Peter's illness – same thing happened to my dad. Very stressful.
Dave