In my diatom culture green algae is growing very fast and some time it will dominate the growth of diatom i diluted sample many times but it is not working
this is a very common problem and it is very difficult to be solved. Back in the day when I worked with algae, an easy method was to treat culture with Hydrogen Peroxide (0.1%) and dark cycles (protect from any light source). Alas, these strategies gave partial advantages, but they were helpful.
The most simple way would be to re-pick the diatom and grow them in f\2 medium. Also after picking the cell give it some wash in sterile sea water to avoid contamination.
It also depend if the diatom is having this green algae as symbiont. Check this out too.
I think its too hard to remove greens from Diatoms,We know the opposite case when diatoms been pollutant you can treat them with Germanium dioxide ,but I think you can reduce greens by limitation of light (in Dark conditions),here greens will inhibit