Good to know this can be a problem. Just to clarify a few things, firstly hydrogen peroxide does not produce ozone. Secondly, the death of cells could not be due to catalase activity, but the lack of it. Catalase preserves cells by safely decomposing peroxide. If there is just too much peroxide around or the cells were already compromised in some way, the free peroxide may have been left to further react to chew up parts of the cell, triggering cell death and overall damage to the plant.
As I understand it, UV light and dissolved metal ions (iron in particular) aid in breaking up hydrogen peroxide, releasing hydroxide radicals. These radicals immediately react with whatever they can causing a radical chain reaction that can wreak havoc for organic life.
The algae are generally more sensitive to this due to the smaller size and simpler cell structure. They cannot cope with cell loss like more complex life, plants, can. Perhaps HC is just more susceptible to peroxide due to it's size? The small leaves just get demolished and that part of the plant struggles to provide food to grow and repair the damage. This idea might be supported by the fact that the smallest portions of the plant, leaf and root tips, appear to die first.
reports found that even at a mere 0.2%, brown algae and some cyanobacteria (blue-green algae) could be irradicated. It was also shown that up to 0.6% exhibited almost no negative effect on larger organisms.
Science rant over.
May I ask what concentration of hydrogen peroxide you were using? 3%? If more than that, maybe try a smaller percentage or try diluting it to treat HC.