I'm sure the PTs here will have more helpful advice, but...

Don't some leg extension machines have an adjustment that allows you to limit range of motion? This could make it safer for your knees I think.

It seems odd that they have you doing weights on back to back days. Maybe the PTs can shed some light on this. Are the weights super light, so they almost mimic the stress of everyday activity more than creating a strong training-type stress???