Even though Jehovah's Witnesses consider themselves to be Christians, they believe that many things are wrong. Jesus did not say it is wrong for Christians to accept gifts. However Jehovah's Witnesses believe it is sometimes wrong to accept gifts. 
Jehovah's Witnesses consider the intent behind your gift and what a gift symbolizes. For example, because they believe that celebrating the holidays is wrong, they will not accept holiday gifts if they're a zealous, active Jehovah's Witness. In case of holiday gifts they will generally wait and see what happens when they tell you they can't accept your gift. If you say that it's really not for Christmas, Easter, or some other holiday, but you just want them to have it for no particular reason, their conscience might allow them to take your gift.
Jehovah's Witnesses can give and take gifts when the gifts are not associated with any religious holiday or worldly celebration. Jehovah's Witnesses are separate from the world. As such they do not want to participate in any celebrations or holidays that would link them with the world. They want to remain isolated and loyal to their God Jehovah based on their religion's interpretation of the Bible. They do not consider that God's requirements and their religion's requirements are not the same. For a Jehovah's Witness, rebellion against their religion is rebellion against God
Sometimes Jehovah's Witnesses wonder what your motives are behind giving a gift. For example they might tell you they don't celebrate Christmas. Then you gift them a Christmas gift. To them this sounds like a test. If they accept your gift, they're afraid you might say, 'I thought you don't celebrate Christmas.'. This puts them in an uncomfortable position and they feel they have compromised their faith for financial gain. However if you make it clear it's not a Christmas gift, they may accept it even if you give the gift on Christmas day. It's a matter of conscience, however some Jehovah's Witnesses may feel guilty that they have displeased God. That's why it's best to give gifts to Jehovah's Witnesses before or after holidays. Also when you give a gift, do not wrap it in holiday wrapping paper. Always give gifts out of genuine love, not because it's a holiday gift.
Jehovah's Witnesses can accept gifts for:
The only religious holiday JW's celebrate is the anniversary of Christ's death, - the memorial celebration. However it is not customary for them to exchange gifts at this event.