If your process is 30% efficient, it wastes 70% of input. If you increase efficiency 1000x, it wastes 70% / 1000 = 0.007% of input, so it's 99.993% efficient.
That would be a 1000x decrease in inefficiency. Very, very impressive but not even remotely as impossible as a 1000x increase assuming that you start with more than 0.1%.
I'd expect the headline to resolve to some perspective where the numbers do make sense, in some very special, limited way, assuming that they didn't just roll dice to decide how many orders of magnitude to falsely claim.
Unfortunately, there's a huge crowd out there that combines, in a surprising way, radical science scepticism with radical science optimism. The "science said man cannot fly, then came the Wright Brothers" crowd who refuse all painful achievable improvements based on their hope for some convenient miracle. These headlines are dangerous.
If your process is 30% efficient, it wastes 70% of input. If you increase efficiency 1000x, it wastes 70% / 1000 = 0.007% of input, so it's 99.993% efficient.