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.

We do actually know a bit about Budget’s processes, thanks to the emails you forwarded to me from the Avis Budget employee who got in touch with you, a senior manager for customer advocacy named Justin Bryce.

Mr. Bryce apologized to you and added: “As we completed our investigation, there is enough doubt that this may have been an ABG employee who took your phone. Based on that, I would like to cover the costs of your replacement iPhone 15.”

You also recounted what Mr. Bryce had told you over the phone, that Budget “had not followed customer service protocols in your case” and “would work to improve this going forward.”

I wrote to Mr. Bryce and Ms. Eatedali to see if either wanted to dispute the authenticity of the email or your characterization of the call, but they did not respond. As for the protocols Mr. Bryce mentioned to you, major rental car companies like Alamo and Budget have procedures for missing items, including dedicated lost-and-found websites that allow customers to report and track the status of items left behind. And I hope those protocols also include cooperating with the police when a customer provides the likely address of the person who may have stolen a phone.

In the case of Alamo John, I did get a faster and more detailed response from Enterprise Holdings, which owns Alamo. But it was confusing. Michael Wilmering, a spokesman for the company, sent a statement noting that the company had apologized and reimbursed the customer, and also said that an auto detailer had found the phone while cleaning the car and followed protocol. “He reported the found phone and turned it in to management, which is our standard policy for found items,” Mr. Wilmering wrote.

That’s when things get either mystifying or suspicious. Alamo John forwarded me a long string of emails that shows the employees at the rental car agency put considerable effort into finding the phone, but does not shed light on why the phone disappeared or why Alamo would not immediately replace the phone the company claimed to have found and lost again.

“Unfortunately, the phone was misplaced,” Mr. Wilmering wrote. “This was a mistake on our part. We are able to return the vast majority of lost items to their rightful owners but were unable to do so in this case.”

He did not explain why a new number and name were saved in Alamo John’s phone and why the device was used. He also failed to discuss when this happened — whether before or after the auto detailer turned in the phone.

One other thing did strike me in the exchanges that John had with the staff of Alamo at the Seattle-Tacoma airport: “We have hundreds of items left in vehicles every single day,” wrote one employee, asking for patience in describing the process by which lost items are cataloged in a database.

Apparently, I’m not the only one who leaves an average of two charging cables, one pair of sunglasses and assorted souvenirs when I drop off a rental car.

If you need advice about a best-laid travel plan that went awry, send an email to TrippedUp@nytimes.com.

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