We investigate the mechanical response of jammed packings of circulo-lines in two spatial dimensions, interacting via purely repulsive, linear spring forces, as a function of pressure P during athermal, quasistatic isotropic compression. The surface of a circulo-line is defined as the collection of points that is equidistant to a line; circulo-lines are composed of a rectangular central shaft with two semicircular end caps. Prior work has shown that the ensemble-averaged shear modulus for jammed disk packings scales as a power law, (G(P)) similar to P-beta, with beta similar to 0.5, over a wide range of pressure. For packings of circulo-lines, we also find robust power-law scaling of < G(P)> over the same range of pressure for aspect ratios R greater than or similar to 1.2. However, the power-law scaling exponent beta similar to 0.8-0.9 is much larger than that for jammed disk packings. To understand the origin of this behavior, we decompose (G) into separate contributions from geometrical families, Gf, and from changes in the interparticle contact network, Gr, such that (G) = (Gf ) + (Gr). We show that the shear modulus for low-pressure geometrical families for jammed packings of circulo-lines can both increase and decrease with pressure, whereas the shear modulus for low-pressure geometrical families for jammed disk packings only decreases with pressure. For this reason, the geometrical family contribution (Gf ) is much larger for jammed packings of circulo-lines than for jammed disk packings at finite pressure, causing the increase in the power-law scaling exponent for (G(P)).