The phrase money for old rope has various meanings: a profitable return for little or no trouble; a very easy job; a person or thing easy to profit from or to beat.

The earliest occurrence of this phrase that I have found is from Driffield Coursing Club. “Peter Delmas” in the genial crowd, published in The Daily Mail (Hull, Yorkshire, England) of 15^th February 1927:

The Bookies smelt all the good things. In the Burton Agnes Puppy Stakes there was “Mercenary Mary,” a black, and there was a brown dog, “Leaps Rigg.”
All the bookies . . . some bawled, some shouted . . . some asked in the most gentlemanly persuasive way for you to back “Mary.”
They didn’t give Mary her full name, it would have sounded too Mercenary, too much like money for now’t. You know that song “Mary had a little lamb” . . . a few hundred followed Mary . . . just like a lamb.
It took the Bookies some time, however, before they could get their bags tight on the Mary money for . . . very little . . . well, “money for old rope.”
[…] Then the judge, slippers, slip steward, flag steward, president, vice-president, patrons, stewards, and all the bally crowd, made a fresh move to find a hare that Mary could nicely deal with. It took some time. We all went through one gate, up a forty acre field, across another one, and, mind you, all the time . . . the bookie never stopped whispering, talking, singing, shouting, bawling, “Six to four against Mary.” Up hill, down hill, through the hedge, over seeds, over ploughed land, not a murmur about “Leaps Rigg” . . . Only one chorus from the Silver Ring, “Six to four, Mary.”
It took a long time . . . but the hare was a pal of the other dog, and all the lambs that backed Mary . . . they were all that much wool short.
[…] “Perhaps too, the bookies had big families to keep, you never know,” I reflected.

The second-earliest occurrence of the phrase money for old rope that I have found is from the Yorkshire Evening Post (Leeds, Yorkshire, England) of 11^th December 1929; an article titled Old Yorkshire Yuletide explains what poetry-making contests consisted in:

The practice was to work the local halfwits to the point of reciting verses specially written for them. One great battle of “wits” is claimed for the far-famed “Tom Treddlehoyle Inn” at Pogmoor, though the “Pigeon Pie” at Sherburn “puts in for it” too. The first village dullard had to recite the following couplet:
          On yonder hill there stands a mill.
          If it isn’t blown down it stands there still.
In the excitement of the fateful Christmas Eve he said the second line wrongly, thus: “If it isn’t blown doon it stands theer vit.” This was rank failure, and to Billy Wimple, his exultant rival, the contest seemed “money for old rope.” He had merely to speak these childlike and bland lines to win the prize:
          My name is Billy Wimple—
          On my nose I’ve got a pimple.
He said “wart” instead of “pimple”—of course there’d have been no joke otherwise—and the contest was declared null and void.
With such primitive mirth was Christmas Eve celebrated in the days of pantaloons and harlequins.
Times have changed and wits are sharper, but the village inn remains the home of jesting.

It has often been said that money for old rope is a nautical phrase referring to oakum, i.e. loose fibre obtained by untwisting old rope, used in caulking wooden ships. But the phrase is first recorded in the 1920s, long after the heyday of wooden ships, and with no nautical connotations: the term old rope was probably chosen simply because it denotes something of little or no use, hence of little or no value.

However, the image itself might be connected in some respect with the nautical world. The Devizes and Wiltshire Gazette (Devizes, Wiltshire, England) of 16^th October 1834 reported that “a drunken prostitute, one of the lowest of the drabs of Drury-lane,” had, the day before, appeared before the magistrate at Bow Street, London, for robbing an old sailor, Patrick O’Bryan, of a half-crown. O’Bryan explains that he was in a public house in the morning; he gave the woman a half-crown and bade her “get a quartern of gin for luck and give [him] the change”. But, after drinking the gin, she kept the change and “shot away with all sails set like a smuggling lugger chased by a King’s cutter”. A policeman took her into custody and brought her before the magistrate. O’Bryan declares:

“And now, having spun my yarn, said Patrick O’Bryan, I have one request to make, and I hope your Honour won’t refuse me.”
“What is it you wish me to do?” said the Magistrate.
Patrick—“Let the poor young woman off, and no more about it.”
“What! after robbing you in such an ungrateful manner?”
Patrick—“She certainly did, but I don’t value the money an old rope’s end. She won’t be richer for it, nor I much the poorer; besides your Honour knows ‘to err is human—to forgive divine.’”

The phrase not to value something (of) a(n old) rope’s end, which means not to value something as being worth a(n old) rope’s end, is indeed of nautical origin. It is first recorded in Love for love (London, 1695), a comedy written by the English poet and playwright William Congreve (1670-1729) and first performed in 1695. Ben, a young man “half home-bred, and half-Sea-bred”, is speaking to Miss Prue, “a silly, awkard [sic], Country Girl”:

Look you Young Woman, You may learn to give good words however. I spoke you fair d’ee see, and civil.—As for your Love or your liking, I don’t value it of a Rope’s end;—And may-hap I like you as little as you do me:—What I said was in Obedience to Father; Gad I fear a Whipping no more than you do. But I tell you one thing, if you shou’d give such Language at Sea, you’d have a Cat o’ Nine-tails laid cross your Shoulders.

The English playwright and actress Susanna Centlivre (circa 1664-1723) used the variant not to care a rope’s end for in A Bickerstaff’s burying: or, work for the upholders (Dublin, 1724):

2d Sailor. Nell, at the Ship at Chattam, shall know this.
1st Sailor. I care not a Rope’s-end if she does.