TPS3813: Are WDR and WDT properly connected?

You should be able to connect Vdd, WDT, and WDR all to the same net +3.3V. No 20kOhm pullup should be necessary.

I wonder if this resistor might have a detrimental effect. WDT is supposed to connect to a capacitor, 0V or Vcc according to the datasheet. Indeed, I have here a specimen which generates a pulse train with 10 ms HIGH instead of 3 s and 25 ms LOW. When I short out the resistor , the pulse train is as it should.

Sorry, I am a little confused on the situation.
1. You are correct in the that WDT must be connect to VDD, GND, or an external cap for correct operation (below).
2. I don't understand the need for the pullup, though I may not be understanding your situation completely. While you do have a pullup, it sounds like you are concerned that the 5V might be a degraded 5V seen at the device pin. The WDT and WDR are high-Z inputs and when putting a pullup on them, a good rule to follow is your input impedance of the device should be 10X that of the pullup to avoid degraded inputs. With the way you are connecting the device, you are essentially halving the input Z, so keep that in mind.

To my understanding WDT is not just a simple input as it will be charging and discharging this optional capacitor, if in use. Therefore it must must be connected directly to VCC or 0V. Now connecting WDR in parallel along with 20 kOhms makes things even worse, as WDR is then presented an undefined level, which is strictly forbidden according to DS. My problem is that management here does not trust me and they will be grateful for a second opinion.