The crunch has arrived. After a vote by Greek MPs, Monday sees the start of the implementation of last month’s EU agreement with Turkey, the process of deporting so-called “irregular” refugees and migrants newly arrived in Greece from Turkey. It is a moment that may come to reshape what we understand by Europe.

It is important to acknowledge how big and generous a role Turkey has played as host for the past five years to hundreds of thousands of Syrian refugees. Under the terms of the deal, the EU agreed to expand cash support to ease the burden. That is not the deal’s contentious aspect. What is troubling, the aspect that raises such difficult questions, is the scheme to deter migrants setting off from Turkey to Europe, and to incentivise Turkish authorities to clamp down on them. The plan to swap each returned irregular migrant for one of the 2 million-strong population of Syrian refugees in Turkish camps, who will be resettled in the EU, is interpreted by some lawyers as a risk of being deported without due process, and is the fear of thousands of refugees and migrants who have already reached the Greek islands – some of whom, like those on Chios, have been rioting at the prospect of deportation.

The promise of the EU deal, struck as popular sentiment against refugees appeared to be spiralling dangerously, was some slowing of the overwhelming flow of refugees crossing the Aegean into Greece. It depended on mobilising EU naval patrols in Turkish waters, in theory deterring people-smugglers and their migrant clients who in turn faced deportation if they made the crossing successfully. But it was always going to be easier for Turkey to take short cuts to fulfil its side of the bargain, thus possibly securing visa-free travel for Turkish citizens to Europe’s passport-free Schengen zone.

As the UNHCR special representative Peter Sutherland argued at the weekend, the deal risked breaching international law banning mass return of asylum seekers, and any returns unless to a safe third country. Many lawyers insist that Turkey does not qualify as safe, a case strengthened by Amnesty International’s report on Friday, which found evidence of the forced return of hundreds of refugees across the Syrian border over the past few weeks. The timing alone, Amnesty argues, suggests that rather than incentivising Turkey to protect refugee rights, the EU deal is incentivising their breach.

There are also reports that the flow of migrants to Turkey’s ports has slowed as the police become more assiduous in their monitoring of traffic. The number of people reaching Lesbos and the other frontline destinations appears to have decreased to something like the rate of a year ago. A Turkish ferry capable of carrying 500 people is docked at Mytilene, the main Lesbos port, and some preparations to process deportees are visible on the Turkish mainland at Dikili. It is claimed that a group of people who have changed their mind about seeking asylum in Greece has been identified and is ready to be returned. In Brussels, prayers will surely be said that these reports are true. This is the only refugee policy on the table; it has to be made to work.

The terms of the EU deal also promised a big push to support Greece’s beleaguered government that has yet to materialise. Hundreds of extra officials promised by Frontex, the EU border agency, have not been seen. Without more support, the business of processing asylum claims and protecting the legal rights of refugees will slow even further. Meanwhile the EU’s other commitment, to speed up relocation and resettlement of 140,000 Syrians who have arrived in Greece over the winter, has also made little progress. EU governments, facing a growing backlash, propose resettling or relocating less than half that.

Greek officials are promising to be sensitive in their implementation of deportations. They – and the rest of the EU – have Europe’s reputation in their hands.