ENCINITAS, Calif. — The surfing Madonna appeared just before Easter weekend and has been stirring a soulful debate in this Southern California beach town ever since.

The striking mosaic of the Virgin of Guadalupe riding a wave was affixed to a wall under a train bridge by artists disguised as construction workers in April. It technically is graffiti that should be removed under the law.

But the surfing Madonna’s beauty is drawing a mass following, and even city officials who say she must go acknowledge they too have been taken by her. They have spent thousands to hire an art conservation agency to find the best way to remove her without causing damage.

The 10-by-10-foot rock and glass mosaic poses an interesting dilemma over whether a city should spend lots of money to get rid of artwork that is illegal but well done and actually beautifies a place.

Deciding what is graffiti is a growing debate worldwide, with guerrilla artists gaining respect in established art circles. A number of museums have brought the street art indoors for prestigious exhibits in recent years, while pieces of illegal art snatched up by dealers have been fetching hefty sums.

Support for the wave-riding Virgin has only flourished amid the controversy. The artwork is on Twitter and Facebook, with a plea: “I’m the Surfing Madonna. Cherished public mosaic. Hangin’ in Encinitas. Hoping to become famous enough to be saved.”

Jack Quick, a local art dealer, saw the men in hard hats put up the mosaic in daylight just days before Easter. He estimates it cost $1,000 in materials and more than 100 hours to build it. The city does not know which artist or artists did the work. No one has stepped forward.

Thousands of people have come to see the artwork. Some have brought flowers and lit votive candles on the sidewalk under her.

Nevertheless, the artwork is problematic, says Encinitas Mayor James Bond, and will put city officials in the position of deciding the taste of Encinitas, which has about 63,000 residents. He added the mosaic’s religious connotations also have drawn complaints.

Some say the artwork blurs the line between church and state; others consider it sacrilegious to have Mexico’s patron saint pictured surfing.

“We can’t just go around saying, ‘Well, when someone slaps up something nice, we like it and it can stay.’ Or, ‘Oh, we don’t like it, so we’ve got to take it down,”‘ Bond said. “We can’t do that with art because people always love and hate the same piece of art. So it’s a slippery slope.”

A Los Angeles-based art conservation agency, Sculpture Conservation Studio, on Tuesday began testing ways to safely remove the mosaic.