要从阵列中就地删除项目，请执行以下操作：
1.用Array::indexOf()查找其索引
1.通过索引Array::splice()删除它

const products = [{"variant_name":"Size","variant_options":["S","M","L","a"]}, {"variant_name":"Size","variant_options":["S","M","L","a"]}];

const removeSize = (product, size) => {
  const idx = product.variant_options.indexOf(size);
  idx >= 0 && product.variant_options.splice(idx, 1);
};

products.forEach(p => removeSize(p, 'S'));

console.log(JSON.stringify(products));

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//get json value from your input
let data = $('#your-input-id').val();

//convert array to json
var parsedTest = JSON.parse(data);

let res = parsedTest.map(val => ({val,
  variant_options: val.variant_options.filter(v_o => v_o !== "S")
}));
console.log(JSON.stringify(res))

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