"I have reminded" is a correct and usable phrase in written English. It is usually used to indicate that you have advised or reminded someone of something. For example: "I have reminded my daughter to do her homework each night before going to bed."
They have struggled with their friends' and family's reactions, and I have reminded them that no one can decide if they should be mothers.
Pauline's fall from grace was one of the most shocking turns, I felt, which I have reminded myself of every time I have felt the flush of success.
Whenever I have reminded him of this, Mr Field has replied that he did so because he thought Mr Corbyn's wing of the party deserved a voice in the contest to succeed Ed Miliband.
To that end, I have reminded all our commissioning editors to ask authors to go below the line, and to liaise with them to find a suitable time to publish each article so that this is more likely to happen.
I have offered Ms Dorries several opportunities to answer the questions I have put to her and I have reminded her of her obligation under the Code of Conduct to cooperate with my inquiry.
I have reminded the founder of Monocle — Victor Navasky, who is fortunate enough to have a Monocle marriage himself — that his brainchild proved to be more durable as a marriage brokerage than as a magazine.
I wish I had reminded myself of that more.
And I've reminded him five times to eat the apple.
I've reminded her she can choose another name and make it legal, but she's opted not to.
I've reminded my students that they can't learn all their music at the last minute.
"I've reminded the boys about that.
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia