Well, it's a fundamental technique in statistical genetics, so the paper doesn't explain it in depth. MR uses the technique of instrumental variables. [1] looks like a good explanation.

The basic idea is to identify a variable Z (genotype, in the case of MR) that causally impacts your outcome Y (COVID, in this case) only through your exposure X (vitamin D levels). If you can find and measure such a variable Z (which meets a few other conditions [2]), then you can robustly identify whether X has a causal impact on Y only from observational data.

[1] https://www.youtube.com/watch?v=NLgB2WGGKUw

[2] https://en.wikipedia.org/wiki/Instrumental_variables_estimat...