In The Handmaid’s Tale season 4 episode “Vows,” June Osborne (Elisabeth Moss) finally escapes Gilead by using a fake ID and disguising herself as an emergency relief aide on a boat headed for Canada, but the ease of June’s escape seems to create a plot hole: how does June’s disguise work if she’s considered Gilead’s Public Enemy #1? Since June successfully smuggled 86 children on a plane to Toronto, it seems unlikely that she wouldn’t be recognized since she’s considered a terrorist after pulling off such a large-scale “kidnapping” and is, therefore, one of the most well-known people in all of Gilead in season 4.
In episode 5, the Gilead Commanders, including a reluctant Nick Blaine (Max Minghella), decide to bombard the war front along Gilead’s contested borders before initiating a temporary ceasefire and allowing international aid to provide relief to the “insurgents.” As a member of an NGO, Moira finds June in the aftermath of the explosion and decides to smuggle her onboard their freighter despite the protests of her girlfriend, Oona. Before the Gilead officers come aboard the boat for a port inspection, Oona makes the last-minute decision to create a fake ID for June and disguise her as another member of their emergency relief staff. When a Guardian questions June about her bruises, there’s a tense moment when the officer appears suspicious of June, but her true identity is never discovered. The ease of June's escape may have been due to Gilead’s own flawed infrastructure.
The Gilead officer may not have recognized June because of the limited information distributed to the war front. After June and Janine escape Aunt Lydia’s custody in episode 3 and stow away on a train headed for Chicago, Nick unofficially discovers through the Martha Network that two Handmaids were spotted near Chicago and he suspects June may be one of them. As the sole commander currently in charge of Gilead’s military operations in Chicago, Nick would be able to control what information is released to the Guardians in the Chicago area. With the intention of protecting June, Nick only appears to share June’s whereabouts with Commander Lawerence, someone whom he believes would act in June’s best interest. With this in mind, the Guardians that intercept their boat along the Illinois coast likely wouldn’t know that June is on the run or have any reason to suspect she’d be in their region.
Gilead’s lifestyle could also be working against them. If the Guardians ever received a picture of June proclaiming her as Public Enemy #1, she'd likely be dressed in her Handmaid garb. Gilead perceives women in absolutes, labeling them either as a Martha, an Aunt, or a Handmaid depending on the life they led before the Sons of Jacob rose to power. According to Aunt Lydia, who preaches Gilead's propaganda, God made June a Handmaid to absolve her past sin of adultery and that service to God is her only significance in their society. It therefore makes sense that the Guardians wouldn’t instantly recognize June in street clothes if the picture that circulated of June shows her wearing the Handmaid’s red cloak and headdress, both of which obscure hair color and tend to obscure facial features due to the long brim.
Since Gilead’s strongest asset is their military, it's almost laughable that their Guardians aren’t able to identify one of their main adversaries. However, Gilead won their past battles against the remnants of the U.S. government through brute strength, not strategy. After the events of the President’s Day Massacre, Gilead's army developed strength in numbers and resources by inheriting the troops from the former U.S. military along with their reserve of weapons. The fact that Commander Lawrence was pardoned from his involvement in Angels’ Flight to serve as a consultant shows Gilead is only now considering changing tactics. There's the possibility then that June's escape to Canada may have been a strategy in and of itself. Gilead has been considering invading Canada to reclaim the children on Angels' Flight since the beginning of season 4 of The Handmaid's Tale and harboring Gilead’s Public Enemy #1 could be the last straw that starts a war.