An alternative cover art was shared by the singer on Instagram on May 17, 2017, showing her lying down wearing a small gauze bandage, and a yellow fall-risk hospital wristband given to patients who are at risk of falling due to lack of balance and weak muscles. According to Collins, the image was shot straight after Gomez came from hospital for a lupus treatment. Alex Frank of "Pitchfork" suggested that it referenced tabloid reaction to the singer's time in rehabilitation. Alex Kazemi of "V" magazine found the artwork powerful and vulnerable, regarding it as the most controversial imagery of a female singer since Fiona Apple's music video for "Criminal" (1997). "Bad Liar" received widespread acclaim from music critics, with some calling it Gomez's best track to date. Upon release, "Bad Liar" featured as "Pitchfork"s "Best New Track" with Alex Frank deeming it as "a victory for an uncomplicated pop star who makes uncomplicated pop music, and a fizzy fun track that will sound as good all summer". In his review for "Rolling Stone", Elias Leight viewed the song as understated, clever and streamlined. Winston Cook-Wilson of "Spin" magazine found Gomez's vocals pristine and the track "charmingly weird", calling its lyrics and sample usage "harebrained but ultimately brilliant". He appreciated "Bad Liar" for eschewing contemporary radio trends, concluding that it "mostly just sounds like itself, and there's no higher compliment to pay it." Writing for "Entertainment Weekly", Nolan Feeney opined that Gomez "found her lane, and she's racing full speed ahead to some of the most unexpected pop music of the year." Jon Caramanica of "The New York Times" regarded the song among the most signature of Gomez's career, describing it as "deceptively original" and "determinedly anti-glossy, as if early DFA Records had tried to reverse engineer a pop song." Caramanica complimented Gomez's singing technique, writing that she "sings sweetly and with clever approaches to rhythm. She doesn't have much power in her voice, but she makes up for that with smart inflections." Joe Lynch of "Billboard" magazine named it "one of the best and most refreshing pop songs of 2017 so far" and "an addictive instant classic unlike anything else on the radio." Raisa Bruner of "Time" wrote the song was a "dramatic departure from her previous work" and "a surprisingly subtle pop song that builds effectively to hit status."