It's not uncommon for an individual to "taste" the metallic filling during the process of removal. Normally this doesn't last beyond a day or so after the procedure.
It is also common when performing a root canal to drill through the older amalgam filling to access the canals but not remove the filling in it's entirety. This is usually because the remaining portion of the older filling is stronger and more protective of the tooth than if it were removed in it's entirety and replaced with the weaker temporary material (the white filling).
You may well be tasting the amalgam filling, the temporary material or a combination of both. While it's unpleasant, this is not generally regarded as unsafe. The element in amalgam regarded as toxic is mercury. but once the amalgam is mixed and set, the mercury is no longer in a "free" state - even when drilled. Thus it isn't absorbed by the body as free mercury. While there is some debate about trace amounts of absorption, research doesn't demonstrate a safety issue. Personally, in my practice, I prefer to err on the side of caution - I do not use amalgam. However, it is widely regarded as a safe material.
I assume when the filling was being drilled suction was used to removed most of the metallic particles. The residual taste can be bothersome, but not a significant danger.
If it is very bothersome, perhaps ask the dentist to remove the remaining amalgam filling and replace it with a harder interim material. This could add additional costand time to the procedure however and it is not the norm. Unfortunately, the most feasible solution is to have the procedure completed, have a new restoration place after the root canal, and tolerate the unpleasant, but not dangerous, taste.
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