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The square box with a cross usually indicates that a character cannot be displayed correctly by the font or does not exist in the list of characters of the font you have selected.
Are you Placing the text from Word or equivalent?
When you highlight some your pink text, does the paragraph and/or character styles show with a little + (override) in front of the style name?
I would try to select the paragraph, clear the formatting and reapply the style with the Alt key down on your keyboard.
Delete the box character. Does the highlight disappear? Then it was only due to this one character missing in the current font, and for some unknown reason InDesign decided to draw such a wide pink background.
Undo the deletion and select the character, then set its font to something with a known wide range of characters -- say, a Times New Roman, Arial Unicode MS, or Cambria. Does something resembling a logical character pop up? (I doubt it, in that position inside a sentence, but you never know.) If so, the character is missing in the current font but still needs to be there, and you'll have to select another font for just the character.
If not, select the character and look in the Info panel for its Unicode value. If it says something like "U+FEFF", "U+FFF2", or "U+E002", then this was probably an invisible dud character in the original text, and InDesign cannot find an appropriate character to display because there is none. Then you can safely delete it.
If not, create a Preflight profile that only checks for "Missing glyphs" (Preflight files in InDesign before handoff to a service provider). Although it would be logical to put that in the Info panel (hint.), rather than plain Unicodes, the Preflight panel correctly lists missing characters by their names. If you see the name of a character that would make sense in here, look for a font – any font at all – that contains the character.
This, for example, is what I get when I read in a linguistics-heavy document into ID, with only default plain text fonts applied:
(Although they all have that pink background, it doesn't generally extend beyond the actual character. That one's really new to me.)