As far as I can tell, feeding the missionaries is not an official church program. At least, I can't find any mention of it in the Handbook. If true, that makes it a church activity organized by the local leadership.
The closest thing I can find in the Handbook is section 20.6.1 on activities: "Members may provide food if doing so is not a burden." Also section 20.2.2: "While gathering in activities can be a blessing, members should not be made to feel obligated to attend every activity. Activities should not put undue burdens on leaders and members."
The Missionary Standards manual, which is aimed at the missionaries, does mention "Meals with Others" and doesn't go much beyond "your mission president and the local stake president will provide guidelines for scheduling meals with people in your mission."
Personally, I agree with the others that assigning people who have not volunteered is likely to create problems. I would raise the issue with local leaders.