Given 3000 tons of gold mined per year, that should be roughly 70 megatons of CO2 / year.
[I am pleased to report that this falls squarely in my previous estimate of 30-150 megatons / year that was based on the cost to mine gold, the cost of fuel, and the CO2 emitted by fuel.]
Bringing this around to carbon taxes, a $20 / ton carbon tax would raise the cost of producing gold by about $16 / troy ounce, and the cost of electricity by around 1 cents / kWh. Googling says it's currently about 700 kWh / BTC transaction, which would create a "carbon surcharge" of about $7 / transaction.
I wouldn't say dwarfed but the answer looks to be ... maybe?
5.8 million tons of junk mail each year in the US. Mass of CO2 to mass of paper looks to be 10.5x for new paper and 3x for recycled, so depending on whether junk mail is primarily recycled or new, that is somewhere between 17 and 60 megatons of CO2 / year.
This here is the problem. Gold does use a lot of CO2 yes (heavy equipment construction and operation), but that's not even the worst thing. Mining literally is poisoning water, and destroying very large ecosystems. And carbon tax won't stop that. And 90% of gold is speculative (if you include jewelry).
Can you quantify the environmental impact of gold mining? How does it compare to the CO2 output of a medium-sized country?