You can set up a Turnitin assignment to exclude quotes, or you can filter these out when viewing the submission. However it is important to note that Turnitin will consider quoted material to be anything within double quotation marks only (“), anything within single quotation marks (‘) will not be considered a quotation. This can cause problems as the Harvard system of referencing, which is commonly used, requires double quotations for direct speech and single quotations for direct text.
This means that a human eye will still be required to check references are accurately given at the end of quoted text, at which point they can then be disregarded. Turnitin is a text matching system based on a computerised algorithm and not a judgement engine, so human interpretations of results are always required regardless of quotes materials.