That is NOT a catalyst, as roelschroeven correctly commented.
Otherwise a rechargeable battery would be a "catalyst" because it too needs to be re-energized or replaced.
What a catalyst does is lower the activation barrier between two states, without providing net energy. Getting H2 from H2O, i.e. electrolysis, requires adding energy. We know this because fuel cells work in the other direction to produce power, and entropy always increases.
Maybe that's now what was meant, maybe they were indeed talking about the catalyst being degraded. But then it's a bit weird to talk about "re-energizing", and more importantly, that still doesn't the main question: what is the energy source?
Am I too hostile towards claims that energy can be made out of nothing? Maybe. I know I don't feel guilty when exposing fraudulent claims.
Some catalysts do get "degraded" over time and need to be regenerated. Look up palladium sintering or zeolite coking. The catalyst itself is not "damaged" but by catalyzing a reaction, its physical shape is altered (get clogged or fused together) which reduce its effectiveness. These can be regenerated by burning off the clogging or heating them up.
And if you get into the enzymes, which are biological catalysts, they are even more likely to degrade and need to be replaced.
Don't try to be smart by insulting others when you yourself are not an expert.