It is "blatant discrimination" to target and punish people on the pandemic unemployment payment (PUP) for travelling abroad, according to an opposition TD.
So far, 104 people have had their payment stopped because of checks at airports.
The €350 won't be made to people who travel abroad even to the green list countries, and isn't paid during the two weeks of self-isolation when someone returns from abroad.
The Department of Social Protection has stressed it will consider cases where somebody has to travel for "urgent or exceptional reasons".
RISE TD Paul Murphy is putting forward a motion in the Dáil to annul the ministerial order that implemented the rule.
Speaking on Lunchtime Live this afternoon, Deputy Murphy stressed that nobody should be travelling abroad at the moment for non-essential reasons.
However, he argued: "What we have here is very blatant discrimination, where those who are on the pandemic unemployment payment - people who've lost their jobs due to the pandemic - are faced with losing all their income if they don't abide by the Government's travel advice.
"If you're a tax exile, Revenue changed the rules for you to make it easier to be a tax exile - if you're hopping back and forth between Monaco and Luxembourg or wherever, there's no punishment for you.
"It's quite incredible they're targeting the one-in-five people in the workforce who are on the PUP. It's not their fault that they're not employed."
He also pointed out that Fianna Fáil MEP Billy Kelleher received 'no punishment' for not self-isolating after arriving in Ireland.
Deputy Murphy said those on the PUP are being "specifically targeted" for a "total loss of income" if they don't follow the travel guidelines.
He observed: "People are in a situation where [they] - having paid for flights and accommodation months and months ago - don't know whether they're entitled to refunds. Unfortunately they're not entitled to refunds - the Government needs to address that.
"The second thing is that instead of having people in the airport checking people's PPS number and checking if people have a job when they're on the way out... instead those resources should be spent on testing people when they're coming in to see if they have the coronavirus, then actually following up."
