Gas hob without burner cover
The burner and gas orifice are configured to give a proper air-fuel mixture so the appliance can safely be used to burn the gas completely into carbon dioxide and water. 

With the burner removed, you won't even have the equivalent of a good propane torch or lab Etna and with an improper air-fuel mixture, soot and carbon monoxide can be part of the resultant combustion output.

Your main problem is that you're trying to use a camp stove/hiking coffee maker on a kitchen range. 

This device is sized for use with alcohol stoves, butane burners, their propane canister kin or propane camp stoves which all have a small burner diameter. 



The best bet would be a sort of conical chimney that sits over the kitchen range burner on top of the grate and funnels the heat up to a smaller grate that your coffee maker sits on. If you look through the various online camping forums, you might find someone already makes these.