A number of resources exist online for finding your retired racer's history. 
Greyhound Pets of America has no affiliation with, or endorsement of, the services listed.  They are provided for informational purposes only.

Greyhound Data provides information about greyhounds from all over the world with pedigree information drawn from the last four centuries.

The internet Greyhound Access Program connects you to the largest collection of Greyhound Racing Data available in the United States.
iGAP is a free download and a subscription service.