There has been some initial opposition to this. One photographer on the threads complained that “there will be a small credit like watermark on the photo, but no link to your account.”
Out of curiosity, I tried out the new feature, went to see if there was indeed a link to the original post, and followed Brianhansel's instructions to turn it off. Here's what happened, and how you can use and adjust the new Threads feature. (All these instructions have been followed using the mobile app.)
The new post will actually only contain the image with your comment and without the previous comment. However, the original poster's name will appear as a watermark in the upper-left corner and the repost's number will appear in the lower-left corner.
Although it's not an obvious feature, there is a link to the original post. When I tapped the watermark, the original post — text and all — appeared directly above my repost.
However, if you want any images or videos you post to be shared with only your original text, you can do so. (Again, instructions courtesy of Brynhansel.)
And that's all. Now, we just have to wait for the next entry in the feature war between Threads and Bluesky.