In reply to matt1984:
I've worked in outdoor retail for 5 years and would personally refuse this as a waranty claim (our warranty department would all do the same).
The rubber has extensive wear and you've actually torn through the rand rubber, after having worn through the edge rubber. You're well beyond the point of an effective resole at this point and any job will be middling at best because they'll have to cut away and patch the whole rand which will significantly change the feel/function of the shoe. Resoles need to be done once the edge rubber wears through and meets the rand rubber below.
The reason the small piece has torn away here is because it became sufficiently thin to rip. This has happened through use and isn't a defect. The rubber on the toe in general is very thin and really on the limit in terms of lifetime anyway. As others have pointed out, the hole itself is also classically positioned in an area where rubber is worn unevenly as a result of foot dragging.
My advice would be to replace your shoes and then to make sure you resole them in future as soon as the edge rubber has worn through. This will allow for a couple of good quality resoles, significantly increasing the value of the shoe and reducing the environmental impact.
I appreciate this probably isn't the answer you want to read but I've found it's best to be honest in these situations as climbers (myself previously included) sometimes have unrealistic expectations about the application of warranty and the lifetime of a climbing shoe. The most effective thing I did was to work on my footwork to improve precision and reduce dragging which means I now get a solid 6-9 months from a pair of shoes before needing resole despite climbing 3-6 days a week.
Hope this helps