NEW DELHI — Every other month or so, someone calls the Rev. Phil Oswald and asks if he would be willing to baptize Hindus so they can become Christians.

“They always follow the same script,” said Mr. Oswald, the pastor of Delhi International Christian Fellowship, a nondenominational service heavy on guitars and jeans. “It’s obviously a setup.”

The Soviets famously used “honey traps,” temptations of booze and beautiful women, to lure Westerners into compromising situations. For some Christians in India, there is a “Jesus trap”: temptations of soul-saving to lure visiting pastors and missionaries into conversions that could cause them to lose residency visas.

Mr. Oswald said he always referred such callers, whom he assumes to be Hindu nationalists, to native Indian pastors who cannot be deported, an offer that is invariably declined. Even so, Mr. Oswald, who is from the Midwest, said his visa applications had faced unusual delays.