What is a "noninvasive" biomarker for a disease?
A biomarker, or biological marker, generally refers to a measurable indicator of some biological state or condition. - Wikipedia


The presence of certain 'things' (sorry for being vague) in a tissue obtained invasively - via biopsy, for example - are considered biomarkers for, say, a cancer. It could be histopathological - a particular abnormality seen on staining the tissue - or it could be the presence or absence of a membrane receptor, etc. 

A non-invasive biomarker is simply one that can be obtained easily and without "harm" to the (patient?), for example, to identify the potential presence of a cancer without the need for a biopsy. (Obviously, this doesn't eliminate the need for invasive methods. It just adds to the arsenal of detection methods.)

That is the usual meaning of non-invasive biomarker in the many, many papers using the term (at least medically), such as the one cited.

Serum microRNAs as non-invasive biomarkers for cancer