Dear Tripped Up,

One day last July, I was dropping off a rental car at Budget’s location at Boston Logan International Airport when I misplaced my iPhone. As best as I can recall, I left it in the car while I went to throw away some trash, but neither my wife nor I nor the employee who was helping us could find it. After my flight home, I began tracking the phone using Apple’s Find My application, and after a trip through western Massachusetts and New Hampshire, the phone began traveling back and forth from an apartment building in Lynn, Mass., to the Budget office at Logan. I reported this to both Budget and the airport police, but the police told me that they could take action only if Budget gave them the name of any employees who lived at that address, and Budget would not help. I want Budget to return my phone or pay for a replacement. Can you help? John, Jacksonville, Fla.

Dear Budget John,

Apologies for the nickname, but I need a way to distinguish you from another traveler named John, who wrote in with a surprisingly similar story about misplacing an iPhone while returning a rental car to Alamo at Seattle-Tacoma International Airport.

Alamo John didn’t immediately notice his phone was gone at the agency and headed off to catch a flight, reporting the loss to Alamo from the airport. A few days later, when he downloaded his iCloud data into an old iPhone his daughter had lent him, he noticed that someone had saved a number into his contacts — with a name he didn’t recognize — and then called it four times within hours after the phone was lost.

So, using detective skills apparently innate to people named John who leave iPhones at car rental agencies, Alamo John called the number and spoke to a man who spoke little English, but enough to get across that he was related to an Alamo employee. (It would turn out that he, actually, was the employee.) Alamo John then reported this to the rental-car agency, but Alamo repeatedly told him over the following weeks that they had not found his phone.

I wrote to Budget and Alamo, and the two companies quickly got in touch with their respective travelers to apologize and reimburse them for the cost of new iPhones — $1,076 for you, Budget John, and $770 for your Alamo counterpart. But it’s one thing for large companies to toss out some cash to avoid bad publicity, and another to explain to me — and Times readers — what happened, and what the agencies will do to prevent similar debacles in the future.

Budget, which is part of the Avis Budget Group, answered my fourth email with a one-line statement from Mariam Eatedali, a director at Edelman, a public relations firm. “Following a review, Budget has apologized” to the customer, the email read, “and reimbursed him for the cost of his phone.” The response did not answer my questions about why Budget failed to report the apparent theft to the police, what went wrong along the way and whether they disciplined or fired any employees.