It is, what it is that China manufactures a lot of stuff today. While we avoid made in China stuff if we can/it's low effort, we also try not to overthink it.
As a default, we generally avoid buying
trinkets as souvenirs that just sit there as we're trying to limit the clutter in the house and conversely, most friends/familiy receiving such a gift won't value it much since it a reminder of our trip, not theirs. Since most of that stuff is made in China, that kind of solves the original problem. However, we're not adverse to buying a small $2 souvenir magnet to throw on the fridge and if we're really feeling adventurous, an ornament for the Christmas tree. Made in China. But the chances I'm going to find a magnet with the image of the Acropolis anywhere but in Athens/Greece is probably unlikely.
If we're getting someone a souvenir from our trip, it's typically local foodstuff like spices, junkfood/candy, turkish delight, hot sauce, wine, etc or something branded like stuff from Harrods' foodhall. With globalization, you can pretty much get anything, from anywhere but I think a consumable can be easily enjoyed and done with.
Alternatively, specific the the OP's original example, a few years ago we bought $15 scarves from a stall in the San Lorenzo street market in Florence to give away as gifts. The labels said, Made in Italy and the vendor said they were made at a factory a few miles away
.Even though we were pretty skeptical at that price, we still bought them. Our friends and family seemed to appreciate them. Handy for our winters in Vancouver or easily regifted.