A soiled paper liner can be dropped down the toilet and flushed away.
Any solids on the fleece liner can be held over the toilet, stretched a bit and gravity should pull it off. Semi solids and breast feed poo might need a bit of encouragement with a toilet brush. Once the bulk is removed from the fleece it can be washed with the nappies.
Both liners put the poo where it should go into the sewerage system and not into landfill.