So believe that God has given me a gift to help people with mental illness. How can I be like "well this is a gift I have from God so you're welcome but don't forget to thank him too" without sounding awkward?
Here is my advice to you. i would stay away from the word gift. Even though you have a gift or have several gifts, saying such will only cause those who have no gift from God, to be jealous, envious, or even depressed. So don't say you have a gift.
If you want to give Jesus the credit, all one needs to do is mention His Name in your comment. here are several examples
"Praise Jesus, that i was able to help you"
"Let us Praise and Thank Jesus , that i was able to help you"
"Thank you, But it was Jesus that put it on my heart to help you"
"The Lord is Good all the time, i thank Him that i was able to help"
For me, i am always saying whatever comes to mind at the time, and always adding "Praise Jesus" to the statment
For example"
"Thank you for thanking me, that was very kind of you, Praise Jesus" or instead of saying Praise Jesus you can say Praise God.
It is Godly to be Thankful towards others. So don't be offended when people thank you for something, even when it was Jesus through you that did it. It is a Godly thing to thank someone. So instead of saying "Don't thank me, thank God" Which i did a lot in my younger days, until God revealed to me that i really should not say that, Say to them it was very kind of you to thank me, but thank God also for using me as a tool to be able to help you.
Here is my story how i learned that it is not really good to say "Don't thank me, thank God"
One day i was driving home from work around 10pm, and the Lord spoke to me, saying "David, the next road left, take it" i said OK Lord. The next road was a gravel road, so i took it. After 20 minutes driving the opposite direction of home, and i had school in the morning, i was thinking maybe i was just hearing things, i am tired, i then told myself the next driveway i saw i was turning around and going home. Then i came to this bridge and there was a girl sitting on the edge of the bridge, my first thought was "Oh my Gosh she is going to jump" i pulled over, and walked up to her, she was crying. Well i am not going to go into detail here about the conversation, so i make a short version now. i wanted to talk to her about God, but she got real upset about me talking about God, when it was God that just allowed her boyfriend and 4 of his friends to rape her and drop her out in the middle of nowhere. So i was at a loss as to what to say if i could not talk about God to her. So i just sat there with her, then God told me to tell her to "Join the military", so i told her that she needs to join the military, she that that was the dumbest thing she had ever heard and asked me to leave her alone, i said dumb or not, it is what you should do. So we sat there in silence for what seemed to me an eternity, but i would not leave until i was dropping her off someplace. Anyways, apparently she joined the military the very next day. Two years later, when i was in the military as well, she calls me at work in Florida, and she told me she had been looking for me for two years, she did not have my name, but she finally found me, she wanted to thank me for her life. She is now married to a wonderful Christian man, and fixing to have a second child with him, and she wanted to thank me for her life. i told her to not thank me, but to thank God, and told her that God told me to tell her to join the military. Then she said, that may be True, but the Holy Ghost put in on my heart to Thank YOU, and i have been searching for you, for two years now, and she said she thanked God every single day for her new life. We talked for a bit and then she hung up. But it was thinking upon the conversation that i repented of saying "Don't thank me, thank God" Because the Holy Ghost, the Spirit of Truth caused her to want to Thank me, and i should not condemn or disapprove of what the Holy Spirit puts on a person to do. It was after that point that i stopped saying "Don't thank me, thank God" that i started saying "That is very kind of you to thank me, and i am thankful that God used me to help you, Praise Jesus"
i hope my advice on this matter, may help you in some way.
^i^ Responding to OP