What this record means
The record shows that QUARRY KIDS was a Principal Register trademark owned by SECOND NATURE DESIGN, INC., but it was cancelled on May 16 2009 because the registrant failed to file a required Section 8 declaration, so the mark is no longer live. It covered plaster or resin giftware, specifically figurines, in International Class 020, meaning a similar name would be most concerning if used for comparable decorative or collectible items. The record does not give the owner control over every possible use of the words “Quarry” or “Kids” in other product categories. Because the registration was on the Principal Register, there is no Supplemental Register sequence to note. The latest meaningful event in the file is the Section 8 cancellation in 2009, and the supplied history shows no oppositions, cancellations by third parties, or other enforcement actions. I'd treat this as a moderate concern if you plan a figurine line under a similar name, but the risk is far lower for unrelated goods.
Informational only - not legal advice.