Are you allowed to use any part of a trademarked logo?

The standard for trademark infringement is whether a mark is confusingly similar to another mark already in use for the same or related goods and services.  Might a potential consumer encountering goods and services under the LuLaRoom trademark be confused about whether the goods and services are being offered by the company that owns the LuLaRoe trademark? In addition to trademark infringement, if the other mark is "famous," one may also have to worry about trademark dilution, i.e., does the mark have a "blurring" effect on the famous mark's reputation, or does it tend to "tarnish" the reputation of the famous mark.  The goods and services offered under the two marks don't necessarily have to be the same or similar for a dilution claim to succeed.