Some preliminary ideas:
- misidentify yourself (eg get a few friends and submit each other's samples)
- mix your DNA with a mammalian organism (something like a mouse). It will get flagged as a bad sample by them probably, due to poor alignment metrics and too many variants, but with the knowledge of which DNA you put in you can do a dual alignment to eg. the mouse and human genome and purify the reads that came from you (there are published methods to do this kind of thing). Not sure how you would get an equimolar mix of mouse and your own DNA, but for $200 you could submit multiple ratios I guess.
- enzymatically modify your DNA. There are some enzymes which cause characteristic mutations. They will turn up as real variants in their pipeline, but you can use the sequence context to filter them out. Kind of like chemical code obfuscation. This would mean extracting your own DNA and treating it, probably not that feasible.