The watermark text is added to the image files during thumbnail creation. Changing the watermark text later won't change the already existing images because at that time the thumbnails are not modified.

But there's the "Thumbnail Creation" tab on the Tidypics plugin settings page where you can re-create the thumbnail of a single image or for all existing images. With the thumbnails newly created they will get the new watermark text.

You can test with a single image (you will need to provide the image entity GUID that you'll find for example in the url of the image entry - the number in the url). If you let ALL image thumbnails re-created please backup the data directory and database first. I don't use the watermark feature myself and had no need to re-create a large number of image thumbnails neither. So, I can't say how long it might take on your site and better have a backup ready in any case!