This is the first I’ve heard of the effect Mars has on Earth’s Milankovitch cycles (unsurprising, given that the paper is recent and the effect is quite small with a very long period). Earth presumably has a similar effect on Mars, but measuring this would be quite difficult. Keep in mind that we’re able to do this for Earth by analyzing drill cores (that paper uses data from 293 scientific deep-sea drill holes), which we can’t really do for Mars currently. Using other methods, we’ve been able to measure the effects of axial tilt and precession for Mars, but the effect from orbital interactions with Earth would be much more subtle. I’d be surprised if you could find anything on it in the literature.
I also would not expect the Moon to make much of a difference. The Earth-Moon distance is <1% of the Mars-Earth distance even at closest approach, so the Earth-Moon system is essentially a point mass to first order. Additionally, the mass of the moon is ~1% that of the Earth, so the effect there is quite small as well. As I mentioned, measuring Earth-Mars Milankovitch cycles is already difficult for Earth (we apparently only recently did so) while likely infeasible for Mars (currently), and detecting the effects from the Moon would be harder still.
I only have surface level knowledge of String Theory, but my understanding is that strings vibrate in simple harmonic motion and that different frequencies correspond to different particles. Since idealized springs are simple harmonic oscillators, you could perhaps say that, in some sense, the strings in String Theory are springs.
But maybe that’s what inspired your question. If you’re asking why they can’t be springs in a more literal, geometric sense, then I would speculate that it’s related to the world sheet that a spring would trace out as it propagates through spacetime. A world line describes a trajectory of a point particle not just through space, but through time as well - thereby describing the history of the particle’s motion. In quantum field theory, these world lines are used in Feynman diagrams to describe interactions between particles. However, these diagrams always have sharp interaction vertices. In other words, the interaction occurs at a specific point in spacetime, which is problematic in terms of relativity (different observers should not need to agree on when a spacetime event occurred). For reasons I don’t understand, this can give rise to infinities (ultraviolet divergences) when doing certain calculations. These have to removed through renormalization, but apparently this doesn’t work when trying to develop a quantum theory of gravity.
In the case of a one-dimensional object like a string, instead of tracing out a world line, it traces out a two-dimensional surface called a world sheet. A consequence of this is that the sharp vertices of Feynman diagrams disappear: while an interaction did occur globally, it did not occur at a specific point in spacetime (different observers will see the event occur at different times, so no relativity issues). This eliminates the ultraviolet divergences and the need for renormalization (again, apparently), allowing for a full quantum theory of gravity. If you were to change the geometry of the strings to something more spring-like, my guess is you would no longer get this nice behavior.