Just to be clear, and without wanting to annoy:
There is no such thing as "voiding the warranty" as was proposed. I may be accused of being pedantic... but this is important for every consumer to understand. Much blood and money was spilled to come up with the Magnusen-Moss act. And it is meant to protect the consumer from manufacturers denying claims simply because the consumer may have modified something that did not affect the component in question.
This idea of "will void the warranty" is something that the manufacturers of various products have conjured to protect themselves. And this concept is no longer legal to present to consumers. There is nothing you (as a consumer) can do to void a warranty. The warranty is what it is, regardless of consumer action.
Now... a manufacturer does not need to repair or replace something under their warranty if it can be proven that the consumer purposefully modified something that negatively affected some other part that the consumer wants fixed, or is itself being claimed as a manufacturing defect. And again, this does not "void the warranty." In fact, this situation is an integral part of the warranty.
Just because I know the law, does not mean that I don't care. (in fact, I'm pretty sure that's the opposite) And my example of a consumer modifying a light and having the manufacturer deny a claim for failed suspension is quite relevant. If you modify something in your car, it never "voids the warranty." It simply means that the manufacturer has to prove that any modification you performed resulted in the failure of the part for which you are claiming warranty coverage. And if that isn't possible, the part must be covered under the offered warranty.
In your example of the mat beginning to tear (presumably at the hole where you removed the logo), there's a good chance that the mat will not be repaired or replaced. And that is NOT because the warranty was voided, but because under the warranty, the manufacturer is not responsible for the failure. (that said, any manufacturer with good customer service would replace this. But under law, they likely would not be required to do so).
Now, if you removed the logo, and the top edge of the mat began to curl, it it started to tear somewhere away from those holes... there's precious little chance that it can be proven that removal of the logo was responsible for this failure.
I hope that's more clear. But I fully admit that it was typed well after beer o'clock.