Let's note that you are not, to our knowledge, experiencing a physiological iron deficiency. Your program is reporting a deficiency of iron in your diet. These are distinct issues, and the latter does not yet suggest a need for supplementation.
The first and easiest steps are:
- Increase your dietary intake of animals, such as with meat and milk and eggs
- Use iron cookware
NB: the latter will, I expect, not be recorded by your program.
NIH's Office of Dietary Supplements notes the difference between heme and nonheme iron:
Heme iron is derived from hemoglobin, the protein in red blood cells that delivers oxygen to cells. Heme iron is found in animal foods that originally contained hemoglobin, such as red meats, fish, and poultry. Iron in plant foods such as lentils and beans is arranged in a chemical structure called nonheme iron . This is the form of iron added to iron-enriched and iron-fortified foods. Heme iron is absorbed better than nonheme iron, but most dietary iron is nonheme iron .
They then present tables comparing heme and non-heme iron derived from various foods.
It's also interesting to keep in mind the amount of iron you actually use is different from the amount you ingest, due to the body's autoregulation. Per Wikipedia:
The amount of iron absorbed compared to the amount ingested is typically low, but may range from 5% to as much as 35% depending on circumstances and type of iron. The efficiency with which iron is absorbed varies depending on the source. Generally the best-absorbed forms of iron come from animal products. Absorption of dietary iron in iron salt form (as in most supplements) varies somewhat according to the body's need for iron, and is usually between 10% and 20% of iron intake. Absorption of iron from animal products, and some plant products, is in the form of heme iron, and is more efficient, allowing absorption of from 15% to 35% of intake.