There is no cause for alarm. Heme and non-heme refer to absorbability, not quality of iron. Iron absorption depends in part on its source.
Iron occurs in two forms in food. Heme iron is found in foods derived from animals, such as red meat, poultry and fish. Then there is non-heme iron, which is found in both plant-derived and animal-derived foods. On average, 10 percent of the iron a non-vegetarian person consumes is heme iron. The body absorbs heme iron very well — it absorbs 23 percent of it. Between 2 percent and 20 percent of non-heme iron is absorbed, depending on dietary factors and the body’s iron stores.

So, if you are a vegetarian, you still get iron from your food, but it is absorbed less readily. Factors in food that improve non-heme iron absorption are vitamin C, citric and lactic acid from foods (fruits and dairy), stomach acid and sugars, particularly the sugars in wine.

Factors that inhibit iron absorption are phytates, and too much fiber and tannic acid (found in tea).

In order to optimize you iron intake, eat beans, peas, tofu and other soy products, spinach, broccoli and tomato juice; select iron-fortified cereals, breads and grains; and drink less tea with meals and more wine! If you need it, your body can absorb a multivitamin or iron tablet.