If you have a look through the information provided by the page you linked, they state:
Our patches are made out of citronella, lavender, and lemon
These three plants all exude chemicals (citronella, geraniol and linalool respectively) that are known to inhibit the ability of mosquitos to find people in certain concentrations, however in general these are thought to have more or less the same efficacy as DEET and similar compounds, but are more volatile and thus are effective for a shorter time.
The general advice for mosquito repellents is to apply thoroughly to all exposed skin. Tests done with patches and other devices that do not cover the whole skin indicate that these are usually less effective than contact repellents (see table 1 and text for description of devices). The only substantially effective personal wearable in the above study was one that fogged the spray in an area around the wearer. Patches and similar devices were about 25% effective (i.e. not very).
In conclusion: These patches will work to some extent, but likely to be very limited, possibly only to the area where they are applied. Although "natural" ingredients do work, they need to be applied to the exposed skin regularly for them to be effective.