I don't think anyone realized that transits of Venus (which are naked-eye observable, but very rare: sort of a pair of 'em separated by 8 years, then a ~120-year gap until the next one) existed until Halley, IIRC, predicted them in the 1600s. Transits of Mercury are rather more common, but it takes a telescope to see those.
Transits of Earth as seen from Mars do occur, but those are separated in time by multiple centuries. Assuming you can see the Moon from Mars (more on this below), the Earth & Moon are far enough apart that it would be obvious that Earth has a companion.
Earth's disk is bigger than that of the Moon by a factor of 7.35 (comparing areas of circles there), and Earth's albedo is about 2.5 times larger, but clouds are brighest, land next brightest, and ocean darkest, so its apparent brightness would depend on weather and what part of Earth was facing you at the time. The Moon is smaller and darker but its surface is much closer to uniform in its reflection properties. I could find a reference stating that Earth gets about as bright as apparent magnitude -2.5 as seen from Mars, but wasn't able to find a statement about the Moon's apparent magnitude; depending on how all that gangs together the Moon may or may not be naked-eye bright from Mars. I think details are going to matter, and I was being very fast and sloppy in this estimating. Another influence is whether the Moon is at elongation or not at the time the Martians were looking; I think maximum elongation would put the separation of Earth and Moon at about 0.08 degrees, which you can see if your eyes are good. Whether you could make out faint Moon that close to bright Earth is more a visual perception question, and I can't answer that one.
(I gave all this some thought last time I was building a FRPG world and thinking about making astrological influences matter.)