The satellites of Mars might be captured asteroids. But Phobos has an eccentricity of $0.015$, and Deimos of $3\times10^{-4}$. If they were captured, they likely were captured with rather eccentric orbits. How did their orbits circularize?
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Astronomers are not still completely sure that these satellites are captured asteroids (see for example this paper). However, in case they are, it's true that their eccentricity should be much higher. There are several theories that provide scenarios for the circularization of the orbits (the most recent I found is this one, which invokes impacts on the moons causing them to start tumbling and exciting the spin), but more data is needed to test these hypothesis (see this last paper for a review of this).