^ From General Relativity theory, using the Swartzschild metric, the maximum deflection angle for light rays grazing a body is given by 2GM/rc^2, where G = gravitational constant, M = deflecting mass, r = radius of deflecting body, and c = speed of light.
For the Sun, the maximum deflection angle is 0.875 seconds of arc - in other words, miniscule. The maximum deflection angle for Jupiter would be about 100 times smaller (M/r for Jupiter is about 1/100 compared to the Sun; G and c are constants). For the Earth, the maximum deflection angle would be about 3000 times smaller (M/r for Earth is about 1/3000 compared to the Sun). For a significant deflection, you need a really big mass and preferably a small radius. Assuming any matter in orbit around the star has a density similar to that of the Earth and is approximately spherical, M/r scales as r^2, so the angle of deflection would be 1/100 that for the Earth for a body with 1/10th the mass of Earth; 1/10000 for 1/100th the mass and so on.
Really, you're overthinking this. The dips are due to nothing more than light being blocked by opaque matter passing in front of the star (recent observations have demonstrated this). Any mystery lies in the depth of the dips and their lack of symmetry - neither of which observations your hypothesis would explain.
For the Sun, the maximum deflection angle is 0.875 seconds of arc - in other words, miniscule. The maximum deflection angle for Jupiter would be about 100 times smaller (M/r for Jupiter is about 1/100 compared to the Sun; G and c are constants). For the Earth, the maximum deflection angle would be about 3000 times smaller (M/r for Earth is about 1/3000 compared to the Sun). For a significant deflection, you need a really big mass and preferably a small radius. Assuming any matter in orbit around the star has a density similar to that of the Earth and is approximately spherical, M/r scales as r^2, so the angle of deflection would be 1/100 that for the Earth for a body with 1/10th the mass of Earth; 1/10000 for 1/100th the mass and so on.
Really, you're overthinking this. The dips are due to nothing more than light being blocked by opaque matter passing in front of the star (recent observations have demonstrated this). Any mystery lies in the depth of the dips and their lack of symmetry - neither of which observations your hypothesis would explain.