Hamilton took out his earrings for the inaugural grand prix in Miami eight days ago
Race director Niels Wittich reiterated before the Miami Grand Prix that it is prohibited to wear body piercings or neck chains in competition.
Lewis Hamilton responded by saying the sport had "bigger fish to fry".
Mercedes' Hamilton agreed to remove his earrings in the car for the Miami race.
"It is a rule for the right reasons," said ex-F1 driver Wurz, who is heavily involved in driver safety and education as the GPDA chairman.
"I would have probably liked a slightly different approach of how to deliver the message."
Seven-time world champion Hamilton has several piercings, and in a bid to resolve the stand-off, the FIA gave the 37-year-old Briton a two-race exemption for a nose ring, which he says cannot be removed.
The ban on jewellery, as well as the wearing of non-compliant under-garments, has rarely been enforced by the FIA but following the race director controversy at last year's title-deciding Abu Dhabi Grand Prix, Wittich has taken a stronger approach.
The FIA says its decision to strictly apply its long-standing ban on matters such as jewellery in competition and non-compliant underwear is a safety issue to ensure drivers are as effectively protected as possible in the case of fire.
Wurz added: "I don't want to end up in football where there are more hands in the air and verbal abuse... you have to work together. It's a style I would have preferred in this case."
Formula 1 heads to Barcelona this weekend for the Spanish Grand Prix.
-- Courtesy of BBC Sport