If we don't use the deluxe products we bought to efile, and ended up printing and filing by mail, can we get a refund on the price of the deluxe version?

[SteamTrain]

No

For the Online software.......the fee is for the use of the software to prepare your taxes....whether they end up being e-filed, or printed and mail-filed is immaterial to the software charges you end up paying. 

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Only the Desktop program has a completely separate state e-filing fee that can be avoided by mail-filing  (except NY  where state e-filing is free )

[Critter-3]

For the future ... 

If you qualify   you can use one of  the 10 IRS FREE FILE options to file a fed & state return for free ... but you must log in thru the IRS site :

https://www.irs.gov/filing/free-file-do-your-federal-taxes-for-free

 For Filing Season 2021, you must make $72,000 or below to use one of the 10  IRS Free File partner offers.

If you choose the TT option then you can log in with your same user ID and agree to switch to the FREE FILE option then your progress will be preserved.