You may want to do the DE filter test. All this requires is buying the smallest bag of DE filter powder you can, and adding a coffee can full of DE to a skimmer, when the pump is running, and then watching the pool returns for 5 minutes or so.

If DE powder shoots back into the pool -- your filter needs work (probably, more sand), and will not be able to remove dead algae from the water effectively. If the DE remains on the filter (as it should), it will temporarily boost your filter's ability to remove fine particles, including dead algae, but will also cause the filter to stop up more quickly and to need backwashing, sooner. So, watch your filter pressure gauge.