Should I tell my management that another one of our other stores is talking trash about us?

TsundereMatrix
I work at a electronics retail store as a cashier. We have a lot of other stores around the country as well within my city. I got a bonus for working over the holiday and corporate gave me a $10 store gift card. I usually don’t shop at our store. The only time I go there is to work. I was headed to another part of the city to do some shopping and decided to stop by one of the other stores and use my gift card. They had no idea I worked at another store and just treated me like any other customer.

They were having system problems and had to call in to get it working. As they were waiting on hold, the one girl pulled out her phone and started showing her coworker video footage of my stores warehouse (not my department) and talking about how crap it is and how disorganized our store is. It was awkward but I do have to admit their store was more organized than ours. My administrator’s name came up (the lady who hired me) and they trash talked her.

I don’t know if I should tell my administrator about this trash talk or just pretend I didn’t hear it. If they ever come to my store again when I’m working and recognize me as the customer that they trash talked in front of, I don’t know what will happen.
Updates:
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I ended up telling my management. They didn’t really care but were just curious about what was said about them.
Should I tell my management that another one of our other stores is talking trash about us?
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