You can check some settings in MS Word to see if this is what is causing you issues.
In Word click the File, then Options. At the left side of the dialog box click Proofing, and then click AutoCorrect Options. The tab you want to look at on the dialog box is called AutoFormat As You Type.
Notice the “Straight Quotes” with “Smart Quotes” check box. This controls whether Word converts your quote marks and apostrophes as you type them. If this is ticked, then when you type apostrophes, they will change to curly ones.
In my experience, this only affects whether Word will allow you to type these characters directly, not whether you can paste them into your document. If it were changing “straight” quotes into “smart” quotes, I wouldn’t be surprised, but it seems to be doing the opposite for you?
It may also help us to know what unicode value is being used for your apostrophe. In Paratext, highlight the apostrophe character and hit Alt+X. This will display the character’s unicode value.