In general I don't see why someone would try to imagine these things with strings and make his/her mind more confused over it. Especially when he/she doesn't have the appropriate basic knowledge on the field apart from maybe some scifi books.
We know that mass and energy are able to act as sources of gravity, because of the Einstein Equations of General Relativity. From the one side of your equations, you have the Einstein tensor which contains the information of your spacetime geometry. On the other side, you have the energy-momentum tensor which comes straightforward from the existence of matter and/or radiation. It's due to this that you actually have that mass,energy can interact with spacetime curvature (
so spacetime is not unaffected from matter). Why do you get this result? The Einstein equations don't need the strings to be extracted. You extract them from minimizing what we call the "Action" in classical mechanics. Strings only come into play as a candidate to quantize gravity.
To quantify this for you, imagine that you have A=B... A corresponds to the geometrical features of the spacetime, and B to the matter and radiation content you consider. If you change B, A will have to change too so you keep the equality. Of course the relation is different:
G_{\mu \nu}= 8 \pi G T_{\mu \nu}
with G_{\mu \nu} the Einstein tensor, T_{\mu \nu} the energy momentum tensor and G the Newton's gravitation constant.
When you want to talk about neutrinos passing through matter, well that needs extra knowledge on the physics of particle physics. Indeed the neutrinos can pass through matter, but that doesn't mean that a huge (super-huge) amount of neutrinos couldn't possibly cause some change in your spacetime curvature. However, when one talks about neutrinos interactions, he doesn't have in mind gravity- because their gravitiational interactions are very small in power compared to weak interactions they are subject to (to an order of 10^{-25} at "normal" energies-
http://en.wikipedia.org/wiki/Fundamental_interaction). The weak interactions however are so rare, that neutrinos indeed pass through matter unaffected. Or another way to state it, is by saying that the probability for a neutrino to interact is actually so small that in general, most of them, can pass through whole planets unaffected. Because of that, just seeing particles as small balls of some mass colliding with other balls, is actually a wrong idea - maybe this works only as a limit approximation and only "effectively".
On the other hand, as photons, so neutrinos can be subject to spacetime geometry, and so they follow the paths they do- for example their trajectories can be bend from a gravitational source (like a heavy planet, star or so on).
