Some members and non-members of a church direct funds to a ministry overseas, partly because they want to get a tax deduction by giving it through the church versus giving to the overseas ministry directly. The church has elected to include the foreign ministry in its missions budget, albeit with a much smaller amount than what is being designated by other people. Does this pose any problems that the church should be aware of?
With the church as the organization overseeing the support of the overseas work (it obviously endorses it by virtue of its own giving), it's almost certainly better to contribute in this manner than by individual donors trying to make wire transfers (I suppose) to a foreign ministry.
In my experience, the typical concern the church must have is that it does not become a conduit for the otherwise non-charitable obligations of individuals who are not really donors.
Let me illustrate. Imagine that a parent is obligated to pay on the college loans of a child who because of his or her mission activity has little income to pay the loans. By "donating" to the church the parent gets a tax deduction. Yes, the income is taxable to the child, but if he or she is a low-income (or, more likely, a high deduction) taxpayer then the "gift" may produce little or no tax to the child. The church has unwittingly become a conduit for the parent's otherwise personal obligation. That's why I believe it is important that churches carefully monitor excessive contributions to funds that benefit their family members.