Noise from diff/transfer case after gear install

[818Gladiator]

I have developed a front end noise or transfer case noise after installing 5.13 gears on my manual gladiator sport. The shop says the noise is coming from the transfer case and it may have been damaged from not programming jeep to 5.13 gears right away. I have drove 100miles, I did forget to program the jeep after picking it up, but it’s a manual. I did program it now, but I put it in 4WD and drove 10feet before it was programmed and that’s when I noticed the noise. Would this cause transfer case damage like the shop is claiming? It sounds like a clicking noise at low speeds and it starts when you turn the wheels. I’m having a hard time believing it’s the transfer case but maybe there is something I am missing. There was no noise or damage before gears, truck has 12,000 miles. The clicking starts in 4WD when the wheels are turned slightly

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