Protection diodes for Arduino pin passing current to +5V rail when powered down - what to do?
Fortunately that is likely an analog input, so a 1 K resistor is about the limit or you could go up to 10 K and be done with it. If you can sequence OFF your signal source seconds before the Arduino is powered down, that would be a safe move.

Since you do not have a capacitor filter on the input pin there is no problem of it discharging through the pin when the MPU is powered down.

Another solution is to use a 2N3906 PNP with its emitter at the pin, its collector grounded, and a 22K resistor from base to Vcc (5 V). When power is shut off the base voltage drops below any existing emitter voltage quickly and the transistor grounds out the pin. It will easily handle any current passing through the 1 K resistor.

However, you have BAT54 diodes with a low Vdrop, less than the BE junction of a PNP, so I think the upper diode will protect the input pin very well.