The Wikipedia Article on this song makes no mention of Dylan:

"l'll Remember You" is a song written by Kui Lee in 1964. Many artists including Elvis Presley (1966), Andy Williams, Tony Bennett, Herb Alpert, and Roger Williams covered it, and it was also performed by Tommy Sands in the 1968 Hawaii Five-O episode "No Blue Skies". Perhaps the most famous version was by his friend Don Ho, who was an aspiring singer at Honey's Nightclub, where Lee worked as a doorman and which was owned by Don Ho's mother.

Frank Sinatra's daughter, Nancy Sinatra, visited 'Honey's' with friends. Hearing Don Ho perform and watching his ease with the patrons of the club, she reported Don's uniqueness to her father who had just started his own record label. Don Ho and his musicians recorded their first 45rpm for Reprise Records the following year; "Tiny Bubbles" and "I'll Remember You" on the flip side.

Several years later, Don Ho was performing in Waikiki as the headliner of Duke's in the International Market Place. Don performed twice nightly (though there were times he didn't leave the stage). His "Suck 'em Up" (late show) was often standing room only. Many musicians who knocked off their hotel lounge gigs by midnight, would drop in to perform. It was the hottest entertainment at the best prices in town, and often went on long after the club was scheduled to close.

Hawaii was a staging ground for the Vietnam War, for many U.S. military personnel. As such it was the last U.S. soil many personnel left, and the first when returning home. The United States military afforded combat-duty personnel a two-week leave in mid-tour. Often the military allowed Military Air Command flights for both husband and wife to meet. Their most popular stay was at the Hale Koa Hotel in the heart of Ft. Derussy, a relatively short walk from the International Market Place. The lure of Hawaii's best entertainers and all one could drink for $5, made Duke's legendary.

Don often closed the "Suck 'em Up" show by performing the song "I'll Remember You". For those service personnel about to be sent back into war and their wives soon to be thousands of miles away, this song resonated with many. Elvis Presley had an affinity for the Islands and gave the song a broader audience. An insert in a mid-1960s movie, it was a stunning benefit concert in Honolulu six years later, Aloha from Hawaii Via Satellite, that catapulted the song's popularity. Within the next few years, the song had been recorded by several well-known singers of the period.

Kui Lee was a prolific composer, writing many songs popular in Hawaii. Knowing of a late-diagnosed terminal illness, this song was written/dedicated to his wife and three young daughters. Kui passed within a couple years of penning "I'll Remember You".