I'm still not sure about the shoehorning of Mongolia into the discussion, but what these sorts of comments often fail to discuss is what the supply chain into new things looks like, because that can be equally destructive to the environment.

Generally, recyclers will pay for scrap that has minerals which can be recovered from the scrap.

Toyota Siennas use liquid Ni-MH batteries. It is likely these batteries as scrap aren't being exported, or, if they are, they are exported to foreign recyclers (in this case, many of those recyclers are actually less polluting that U.S. recyclers simply because they built their plants this century and new technology pollutes less). Also, Ni-MH can be replaced one cell at a time to produce "rebuilt" battery packs sold to economy customers, and "spent" cells, which simply fail performance tests, can often be used in other applications that are less demanding than hybrid vehicles. There is a cottage industry here in the U.S. doing these things. Ni-MH that is exported is usually completely dead cells going to a recycler (smelter), or at least that was my experience when I worked in that supply chain.

Li-ion using Cobalt is highly sought after by recyclers due to the expense of virgin Cobalt, so experiences a similar supply chain to Ni-MH. LMO chemistry batteries were the ones nobody wanted to touch, as they have no value, and they are all of the cheap replacement batteries people buy on Amazon for $15, and likely will be the chemistry people will use in their EU mandated replacement battery phones for some nightmare future mass pollution disasters.