When the woman was having her baby and that midwife kept saying "It's okay, it's okay." Absurd.
Also, no one used the word "Pilgrim" to describe them until a century or so later. They certainly did not call themselves that. They called themselves Brownist Separatists.
Origin of OK
initials of a facetious folk phonetic spelling, e.g., oll or orl korrect representing all correct, first attested in Boston, Massachusetts, in 1839, then used in 1840 by Democrat partisans of Martin Van Buren during his election campaign, who allegedly named their organization, the O.K. Club, in allusion to the initials of Old Kinderhook, Van Buren's nickname, derived from his birthplace Kinderhook, New York
Origin of OK
initials of a facetious folk phonetic spelling, e.g., oll or orl korrect representing all correct, first attested in Boston, Massachusetts, in 1839, then used in 1840 by Democrat partisans of Martin Van Buren during his election campaign, who allegedly named their organization, the O.K. Club, in allusion to the initials of Old Kinderhook, Van Buren's nickname, derived from his birthplace Kinderhook, New York
There are many theories about the origins of the word, some more plausible than others. The Oxford English Dictionary and the Chambers Dictionary of Etymology agree that it’s apparently an early-19th-century American abbreviation of oll korrect, a jocular misspeling of all correct. Other theories are that the word somehow came from Old Kinderhook, the nickname of U.S. president Martin Van Buren; that it has Native American origins; that it was a Morse code abbreviation; and that it is an abbreviation of out of kash, another jocular misspelling (for out of cash).