ah, that's embarrasing... Thanks for pointing this out!
I have no idea, why I have written that text in German. Probably, it was late at night when I wrote that part of the code... :-) I will of course change that to English (and look for other texts that I might have written in German accidentally.)
So, yes, you can of course change table IDs, that is no problem. (By the way, in TablePress, table IDs can now also have letters in them and are not required to be numeric-only, as it was the case in WP-Table Reloaded. I think that this is pretty cool, as it allows much better IDs :-) )
Now for the actual message: The text means "Do you really want to change the table ID? You will then have to adjust all Shortcodes for this table in your posts and pages!".
So, basically it's just a reminder that just changing the ID is not sufficient, as the table will the not be displayed in the old place, unless the Shortcode is also changed.
And a short note: There still is a small usability problem with this (the function itself works fine!): Depending on whether you clicked on the "Save Changes" button immediately after typing the new ID, you might have to click it again, after confirming the above mentioned message dialog. So, until I find a nicer way, the best procedure is to type in the new ID, click somewhere in the empty area on the right of the "Save Changes" button, then confirm the then-showing message dialog, and then click "Save Changes". Once you see the save confirmation message below the "Save Changes" button, everything is fine and was saved.