If this document was produced by scanning and OCRing text, there's a good
chance that what you're dealing with is frames rather than text boxes. A
frame will have black square sizing handles, whereas a text box has circular
white ones.
If they are frames, they are easily removed by selecting all the text and
pressing Ctrl+Q. This resets the paragraph format to that defined in the
style, which will not likely include a frame. Note that you will lose all
other directly applied paragraph formatting, and the order of the text may
be disturbed, since the contents of the frames will be in the order in which
the frames are anchored in the document.
If the boxes really are text boxes, then you may still be able to use a
shortcut. Double-click on the border of one to open the Format Text Box
dialog. On the Text Box tab, click on Convert to Frame and say OK. Then
click on another frame and press F4. Repeat for all frames (you may be able
to select multiple ones by Shift+clicking). Then Ctrl+Q to remove the
frames.
