Cardiff fear the last six of their personnel to reach the United Kingdom from South Africa will have their isolation periods extended.
The three players and three staff tested positive in South Africa.
Arrivals from a red listed countries must take a Covid test two days later.
"They're carrying Covid so they likelihood is they're going to test positive and have to default to another 10 days," said Cardiff chief executive Richard Holland.
"It needs a rethink and it needs adapting and that's what we're urging the authorities to do.
"Everyone we talk to sympathises and agrees, but what we actually need to happen is something to change and that's what we're pushing for."
The bulk of the Cardiff party arrived in the UK on Friday, 3 December are due to leave their 10 days of hotel isolation on Monday.
However, the six who tested positive had to isolate in Cape Town and are doing so again with a 10-day minimum, amounting to a double isolation.
Cardiff believe the six - and those in similar situations - should not have to isolate again having already done so abroad.
Speaking to BBC Radio Wales Sport, chief executive Holland: "We're not looking for an exemption for Cardiff rugby players.
"We think that the legislation should look after everybody else who's in this situation as well.
"It doesn't make any sense to us and that's what we're challenging."
He added: "Everyone you speak to and the medical scientists will tell you that what they're having to do is crazy, but the legislation doesn't permit for them currently to be allowed to go home.
"So we're working through it and I'm hopeful that we can find some resolution and common sense prevails.
"The message that has to go out there is there's a plan A in place, but there doesn't seem to be a plan B, C or D and we've been in this pandemic now for two years - there needs to be a plan B different eventualities.
"And if you've been diagnosed with Covid and you're certified as having had Covid it actually supersedes a PCR test so in terms of travel regulations the legislation needs to be adapted and amended to look after different cases."
In the absence of the players - and staff members - who are isolating, a makeshift Cardiff team gave a spirited display in their home 39-7 European Champions Cup defeat by Toulouse on Saturday.
Cardiff go to Harlequins in the same competition next Saturday.