Hi Susan,
We can't answer for this particular situation but yes, quartzite can etch and stain. It can depend on many factors, one of them being the treatment/sealer that is applied and eventually re-applied and also the type of stain on the countertop.
Using coasters and trivets can preserve the beauty of the stone.
Since we fabricate and install the countertops, we can not be responsible for the owners particular use of the countertop.
Best regards
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