It is commonly known that price tags increase the risk you run into problems with customs. The reason for that is not only that it shows a number much higher than you declared, it also clearly puts the item in the category "new" instead of "used".
All shopping agents offer a free service to cut them off when you submit it to international shipping.
It's hard to say if it's worth it. First you have to make up your mind if you see cutting them off as a loss. If you don't care, then just cut them off. If you prefer to keep them, the question is how much it increases the risk.
My experience is that the price on the tags was never brought up by customs and I never saw a reason to remove them.
added: 6/26/2023
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Should I cut off the tags?
Should I get the tags removed?
If i choose to order the products with the tags will it have effects on the customs clearance?