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This makes no sense. Being able to store a lot of heat energy is exactly what you want. Of course it takes more energy to heat water than a sheet of aluminum, but which one is going to stay hotter for longer. Any chemical solution isn't going to magically get you more energy out than you put in.
A water bottle (~1 liter Water) need a lot of energy to heat the Water and stores the heat for1 Houre, not more. This patches don't need any energy to heat, no more than the humidity of the environment, to start an exothermic process that lasts between 8-12 Hours, depending on the size of the patch. It requires no more energy than taking it out of the package so that it starts to heat up on its own. It does not require any external energy input, such as heating water electrically, with gas or other fuel, to heat it first, as is the case with the hot water bottle.
You're not considering the energy required to smelt the iron.
Iron filings (in a collected quantity high enough to make manufacturing these heat packs worthwhile) are not a waste product, they are recycled -- saving the smelting of that much new iron.
Sawdust+iron heat packs are a very useful and non-hazardous product, for sure, but aside from situations where a hot water bottle is impractical, hot water bottle still wins.
So.. I really don't know chemistry, and these aren't the highest quality references, but here goes:
Huh. So maybe heat packs are a reasonable use of scrap iron's embodied energy after all. Assuming you have a sufficient source of uncontaminated steel filing waste and that it's economical to collect and process into heat packs.
...But only if you're heating your water using fossil fuels using an inefficient method! If your water is heated using solar or waste heat capture or a heat pump^[4]^, which would swing the balance way over to hot water bottles again.