I'm enclosing my images inside of text boxes so that the images and their descriptive, non-numerical captions (such as "the telescope") will be tied to the image. The problem is that I can't fit the text box border snugly around the image (+ caption) because there's a left margin inside the text box whose width seemingly cannot be reduced. I've tried clicking on the box >> Format Shape >> Text Box >> Internal Margin: Left: 0", but the margin will not go away. How can I get rid of it?

You'd do better to insert the image into a table cell. Not only does this give you greater control over the image size (by fixing the cell height and width), but can also ensure a better fit vis-à-vis borders (or borderless).

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]

Thanks Paul, I'll do what you suggest.