Also, you are probably not really self-employed.  Most pastors are common law employees and must receive a W-2, even though for income tax purposes you pay self-employment tax rather than being subjected to FICA withholding.  Being a common law employee has other implications; your church must follow wage and hour laws, laws on documenting pay and paychecks (this is a biggie in NY for example) and other things.

You will want to read this.
<a rel="nofollow" target="_blank" href="http://www.ecfa.org/PDF/2016-Preparing-Tax-Returns-For-Clergy.pdf">http://www.ecfa.org/PDF/2016-Prep...>

"Church members can give you tax-free gifts, but the church cannot."

Let me expand on this a bit.  Our church collects pastor gifts for "pastor appreciation month."  If the members make gifts of gift cards and money and checks made out to the pastor, and someone holds them all and gives them in one envelope, those are personal gifts even if the gift campaign was arranged by the staff.  But if the money is deposited in the church account and issued to the pastor as a church check, it's taxable compensation.

May I return the check and have them issue cash or gift cards?

No, at least, not practically.  Firstly, the church can't give you cash or gift cards either, it would still have to be on your taxable income and reported on your W-2 or 1099-MISC.  Anything of monetary value that the church gives you is taxable income except for a parsonage, due to old common law exceptions.  

Secondly, if these were gifts from church members and you wanted to return the check to the church, have the church send the money back to the members, and have the members re-give the gifts to you personally--you can't easily do that because it is now after January 1.  If you did that before January 1, the church could have adjusted your W-2 or 1099-MISC to reflect the salary give-back and only report your net salary.  But because the money was paid in 2016 and would be returned (if you did it) in 2017, your 2016 tax documents must reflect what actually happened in 2016.  You would report and pay tax on the income in 2016, then you could take a deduction for the repayment in 2017.  But unless the amount is more than $3000, the deduction is not very effective and your actual benefit in 2017 would be much less than the tax you would owe in 2016.  If the amount of salary repayment was more than $3000, the income tax picture would be a wash (pay income tax in 2016 and get the same net deduction in 2017) but you would still pay self-employment tax on the amount in 2016 and that won't come back in 2017, due to how the repayment deduction is handled on the tax form.

If these are gifts from church members, you can do it tax free next year, but I think you are stuck this year.  And your treasurer needs some training.

Generally speaking, gifts are not taxable to the recipient, nor does the recipient have to report them (unless, in some instances, they are from a foreign source).  [But see Opus 17's correct comments re: gifts to clergy]

Employer can't give a non-taxable gift.

@Opus 17 -- Muchas gracias.

It's not specific to clergy either. My ex-wife works for a grocery store chain that provides employees with gifts cards to buy flowers or food for funerals of close relatives. It's a nice little bereavement gesture, and it is duly added to the W-2 and the appropriate employment taxes are deducted. I had to research this when my church wanted to give a going-away gift to our previous pastor. Basically, any company can only give tax-free gifts if they have de minimis value (t-shirts, mugs, etc.) or if they are part of a longevity award program that applies to all employees with similar longevity. (Plaque at 5 years, clock at 10 years, etc.)