should i transfer this to a better container?

the kimchi my family buys at our local korean mart comes in these plastic tubs. the lid gets pretty flimsy when open and closed repeatedly and not everyone in the house likes the smell so we wrap the container in plastic and store it in a ziplock bag. its starting to feel a little inefficient going through those layers every time we get a serving. would it be advisable to start transferring it to a tupperware? would that affect the fermentation? i hope this isnt a silly question