Suppose you have a pen. A pen has the power to write. But, if you think about it, it can't write on its own; its power to write is purely instrumental. For its writing ability to manifest in action, the pen has to be applied to actual writing: you take it in hand and write with it, thus using the pen's ability to write in order to write. This applicatio virtutis ad actionem, the application of the power to the right sort of action, is one side of instrumental causality.
But you can look at it in a different way, and think of the pen as really having the power to write, in a full sense, when it parcels out, so to speak, or participates in, the activity of a higher power: in this case, your power. When you take the pen in hand and apply its ability to write to actual writing, it has become an extension of your own ability to write. And thus the pen writes, which it cannot do on its own, because it is an instrument of your own power to write.
These points are quite general, and one way to interpret the extended mind thesis charitably from a Thomistic point of view is to see it as a rediscovery of the considerable use by the human mind of instrumental causes, applying various things (like notebooks and iPods) to their actions, so that these things participate in the power of the mind itself, as its instruments. As Clark and Chalmers say (in the paper linked above):
It is not just the presence of advanced external computing resources which raises the issue, but rather the general tendency of human reasoners to lean heavily on environmental supports. Thus consider the use of pen and paper to perform long multiplication (McClelland et al 1986, Clark 1989), the use of physical re-arrangements of letter tiles to prompt word recall in Scrabble (Kirsh 1995), the use of instruments such as the nautical slide rule (Hutchins 1995), and the general paraphernalia of language, books, diagrams, and culture. In all these cases the individual brain performs some operations, while others are delegated to manipulations of external media.
And the Thomist has a reasonable analysis of how this would work in terms of instrumental causality, and even can capture the striking feature of the extended mind thesis -- the apparent extension of the mind into the world -- with the notion of participation, and all in a way that relies less on metaphor and more on actual careful analysis of action than one usually finds associated with the extended mind thesis.