A bad wrap is an unappetizing sandwich made of fillings wrapped in a tortilla. A bad rap—otherwise known as a bum rap—is dishonor resulting from false accusations or trumped-up charges. No hyphen is needed in this noun phrase.
There’s also bad rep (where rep is short for reputation—an abbreviation that dates back centuries), which makes more sense than bad wrap. To have a bad rap is to have a bad rep, but bad rep appears only rarely, and some readers might interpret it as a misspelling of bad rap.
The rap in bad rap is related to an American sense of the word dating from the late 18th century—namely, a reprimand or a criticism. It’s closely related to the rap in rap sheet, which refers to a list of one’s past criminal offenses. All these senses of rap probably descend from older senses relating to blows and strokes delivered as punishment. The fact that rap sounds like rep might also have contributed to the modern sense of bad rap.
Instances of the misspelling are easily found—for example:
I think the guy’s genuinely talented and unfairly gets a bad wrap. [Collider]
Tom Bradley has gotten a bad wrap within the fanbase the past few seasons, stemming from the 2009 Rose Bowl when Mark Sanchez torched PSU for 400 yards. [The Buckeye Battle Cry]
Here the phrase is spelled correctly:
The 250 million cars and trucks on America’s roads get a bad rap for being environmentally unfriendly. [ABC]
For-profit colleges and universities have been getting a bad rap for the past several months for allegedly being diploma mills that provide little guarantee that their graduates will be employable once they finish their programs. [Diverse]
Despite this important role in our society, the media often receive a bad rap. They are often blamed for blowing things out of proportion and causing concern where some feel they shouldn’t. [Seacoast Online]