1995 Dodge Ram Cut in the tire wall

Tires and Wheels problem
1995 Dodge Ram V8 Two Wheel Drive Automatic

I have just had a new tire put on my spare wheel and on my way back home, the wheel and tire fell off. This is a PU truck and the spare is stored under the bed.

As a result, I have a cut in the side wall. At the deepest, the cut is less than a 16th of an inch. It is also about 5 inches long starting at the tread. Definitely not a major cut but I feel like it does make the tire more vulnerable and since it is brand new, I am thinking of asking the shop to replace it.

What do you think?

Thank you.