I use a soapy sponge pretty much every single time I clean my cast iron. Sure, it will remove a little bit of the seasoning (depending on how hard you scrub it, of course), but it’s not a big deal, especially if the pan has been seasoned correctly prior to washing.
Seasoning is, in my experience, best viewed as an ongoing process, not an infrequent task whose results should be sheltered at all costs.
At any rate, you certainly won’t harm your pan by giving it a good scrub – just be sure to dry it thoroughly over flame when finished and apply whatever fat you choose inside and out.
Burning the food off will also work, of course, but I find that this takes off much more seasoning than just washing it as you would a stainless steel pan or such.