I have always kept the clear plastic lids, assuming they made the tub seal.
I happen to have an empty tub at present, until I decide which soap I wish to put in it, so I conducted a highly scientific experiment.
I half filled said tub with water and put the lid on, without the clear plastic bit, turned the tub upside down and shook it a bit. No water leaked, although I could tell when I removed the lid there had been some seepage.
In summary, the clear plastic lids probably aren't required as the lids seal on these pots fairly well anyway, I suppose the pots do need a 100% solid seal in transit though just incase.
Whether you choose to keep the clear lid or not is personal preference, I think following my experiment I'll probably throw the next one away that falls out.