I have done prior posts about mercury and MCS. The short form is from Danger of antioxidants (2016) and treating MCS (2016). Why MCS and mercury? “Our data show an increased prevalence of metal allergy and elevation of mercury levels in bioindicators among patients with MCS.”  If a supplement impacts MCS negatively, then it may also impact high mercury in a similar way (this is a fall back approach where there is a lack of studies).
There are some professional ways to remove it, see eMedicine, but these will only be done when it is clear that the level are very high.
Items to reduce mercury levels
“Other than avoiding potential sources of mercury poisoning, there is no major role for self-care at home.” [eMedicine] ” Currently, no chelation agents have been approved for methylmercury or ethylmercury by the U.S. FDA.” 
- Some forms of mercury will dissolve in olestra  – used for some potato chips
- “The children and pregnant women in the study were found to have elevated blood levels of lead and mercury compared to age- and sex-matched Canadians. Consumption of probiotic yogurt containing 10(10) CFU Lactobacillus rhamnosus GR-1 had a protective effect against further increases in mercury (3.2 nmol/liter; P = 0.035) and arsenic (2.3 nmol/liter; P = 0.011) blood levels in the pregnant women, but this trend was not statistically significant in the children.” 
- Lactobacillus Fermentum ME3  produces glutathione, and per Mercola article “when your glutathione and sulfur levels increase, you’ll typically see higher levels of mercury coming out of your hair… “The core of the detoxification system is the glutathione system,” Dr. Shade says. “Notice that I don’t say, ‘it’s glutathione.’ No, it’s the glutathione system.“
- Effect of Probiotic Bacillus Coagulans and Lactobacillus Plantarum on Alleviation of Mercury Toxicity in Rat . “Oral administration of either probiotic was found to provide significant protection against mercury toxicity by decreasing the mercury level in the liver and kidney”
- Taurine: “Results suggested that taurine played a vital role in reducing the mercury toxicity in intoxicated animals.” 
Items to Avoid
- Grilling fish increases mercury intake 
- Do not go strict Gluten free — Specifically avoid rice and products containing rice.
- The following supplements:
- N-acetylcysteine (NAC). 1998 study found it was effective for removing organic mercury but not inorganic (like from amalgams)
- alpha lipoic acid (ALA)
- reduced glutathione