I ran some simulation of the power recovery circuit in ltspice. With the assumption, that the controller driving the LED baragraph draws 1.2mA at 2.4V, the following peak currents of the power recovery diodes were simulated, and the following harmonic distortion values were simulated as well. Only 3rd harmonic levels below the carrier are shown as they are most pronounced. Long story short, the worst harmonic simulation was 3rd harmonic at -34dB below the carrier. I would say this is a pretty harmless value for a circuit, that is inserted between the transceiver and antenna only during antenna adjustment.
1.2mA at 2.4V is a realistic value if all the AtTiny13A power saving features are used and LED current is limited to 1mA.
At 1W input power:
At SWR 1:1, the diode peak current is 7.4mA, which is 3.7% of 200mA input peak current, and 3rd harmonic introduced by the power recovery circuit is -36dB below the carrier.
When antenna open, the diode peak current is 8,3mA, which is 6.1% of 135mA input peak current, and 3rd harmonic introduced by the power recovery circuit is -34dB below the carrier. This is the worst distortion value.
When antenna shorted, the diode peak current is 7mA, which is 2.9% of 240mA input peak current, and 3rd harmonic introduced by the power recovery circuit is -39dB below the carrier.
At 10W input power:
At SWR 1:1, the diode peak current is 11.5mA, which is 1.8% of 636mA input peak current, and 3rd harmonic introduced by the power recovery circuit is -36dB below the carrier.
When antenna open, the diode peak current is 13mA, which is 3% of 427mA input peak current, and 3rd harmonic introduced by the power recovery circuit is -35dB below the carrier.
When antenna shorted, the diode peak current is 11mA, which is 1.4% of 764mA input peak current, and 3rd harmonic introduced by the power recovery circuit is -36dB below the carrier.
