I don't think they must have finished file project by the end of last month ,______？

by the end of last month ？
与过去完成时连用,所以是had they?
must表推测的反意疑问句的有关用法

1）对现在情况的推测，问句部分用主动词（do,be)一般现在时的适当形式。若是现在进行时，问句部分用现在进行时的适当形式表示。若是there be结构，问句用isn't/aren't there。如：
1)He must be there,isn't he?
2)He must have a big family,doesn't he?
3)He must be waiting outside,isn't he?
4)There must be some students in the room,aren't there?

2）对已发生的过去情况的推测，若陈述句谓语部分有“must have done”，而且有表示过去的时间状语，问句部分用didn't；若没有表示过去的时间状语，问句部分用haven't或hasn't。如：
1)They must have gone there last night,didn't they?
2)They must have arrived by now,haven't they?（根据by now来判断）
3)They must have been to the Great Wall,haven't they?

3）若是被动，应按被动结构来处理。如：
1)The room must have been cleaned yesterday,wasn't it?
2)The room must have been cleaned,hasn't it?

4）若句中有表示过去完成时的时间状语，问句部分应用hadn't.如:
They must have learnt 5000 English words by the end of last term