To slightly add on to what @Rukifellth said. なくては is literally ない + て (form) + は (topic particle). I like to think of て as “and”, tying together two things that are related to each other in some way. But to get into the more literal meaning, I interpret it as as, “in the situation/manner of” (ex: 雨が降っては公園に行けない – “In the situation of it raining, I cannot go to the park” or more naturally “It is raining, therefore, I cannot go to park”).
Here’s maybe a more literal translation of these to kind of see what’s going on:
なければ - Since this is pretty dirty, if I don’t wash it, it wouldn’t be good.
なくては - Since this is pretty dirty, it wouldn’t be good in the manner/situation of me not washing it - OR - Since this is pretty dirty, the situation of it not getting cleaned is be bad.
Notice how when using “in the situation/manner of” we’re basically saying that those two things are directly connected. ては is basically stating a fact (like Rukifelith said), or more specifically, its telling you that these two things are related to each other. Therefore, there’s more emphasis on needing to have the washing be done. More specifically we could look at it like, “the situation of me not washing it would be bad (therefore, I should do it)”. However, with ば being hypothetical, we’re focusing on what would happen if we didn’t do the washing and doesn’t come off as strong.