New Orleans — Patricia Giangrosso honored veterans this weekend the same way she has for the last several years, by “knitting her bit,’’ a program sponsored by the National World War II Museum that provides hand-knitted and crocheted scarves to those who have served their country.

The scarves are crafted not only by local volunteers but also by people from all across the country, and while the museum ships many of them to veterans’ homes for Veterans Day events, they pass them out to veterans who visit the museum.

“I come to honor my father who was a World War II veteran, James L. Giangrosso,’’ Patricia Giangrosso said as she deftly worked her crochet hook, transforming yarn that she described as “Air Force blue,’’ into a warm scarf.

“Last year, I had the pleasure of handing out the scarves, and it has been a wonderful experience,’’ she said. “They were so touched.’’

She was touched, too, most particularly by a very young veteran who seemed to her to have been struggling with his wartime experiences. But the flood of veterans also included many who are clearly enjoying life.

“Some of the really old guys would ask, ‘Can I have one for my girlfriend?’ ” she said with a chuckle.

The museum launched the scarf project in 2006. Staffer Lauren Handley came up with the idea, and the name came from the Red Cross, which used the slogan “Knit Your Bit’’ during World War II, encouraging those on the home front to knit for the troops.

She hoped to perhaps get 50 to 100 scarves. But she vastly underestimated the response.

“They just started rolling in. I got calls from security daily, saying more scarves were here,’’ she said.

In total, the program has produced close to 25,000 scarves for veterans. They are distributed at the museum on special occasions and shipped to veterans centers and stand-down events for homeless veterans.

Handley had about 500 scarves on hand Saturday, and she plans to ship any that are left to veterans affected by Hurricane Sandy.

The museum issues a new pattern every year, available on its website at One year, the design featured a V for Victory emblem. This year’s design is red, white and blue with the letters “USA” featured — inspired by the Olympics, Handley said. The museum also accepts scarves by knitters who use their own favorite pattern, although Handley said that patriotic themes and colors are most popular — even for women veterans.

That seemed to be the case Saturday.

Johnny DiFatta, 87, chose a bright red, white and blue crocheted scarf, which he said he would wear on Veterans Day and other patriotic holidays — and to American Legion and Veterans of Foreign Wars meetings. The New Orleans veteran, DiFatta, who ran Higgins boats in the Pacific during the war, volunteers at the museum frequently.

The knitters made sure to include those familiar faces as well as visitors in the giveaway, one of a number of events planned for the weekend, including a performance by the U.S. Naval Academy Women’s Glee Club and the Louisiana Bicentennial Military Parade passing in front of the museum Saturday. Sunday, the Navy Band New Orleans is scheduled to perform there at 11 a.m.

The knitting project is ongoing, and for Handley, it has turned into something of a community with a group of regular knitters who come to the museum and have developed friendships. She also sees how the effort is bringing people together all over the nation.

Shirley Sentgerath, a woman in her 80s who lives in Michigan, sends about 100 scarves every year. A teacher in Buda, Texas, taught her fifth-grade students to knit and incorporated lessons about veterans. Members of that class sent their scarves to the museum. Groups around the country who adopt charitable projects have sent in scarves. Some have been contributed by families, with notes that the scarves were made by multiple generations.

While the knitters don’t know who will end up wearing their scarves, the recipients get some information.

A tag attached tells who made the scarf, and more important, why — to say thank you.