I would not use the phrase gentle reminder in this context. Your professor could take it as sarcasm rather than a sincere desire to nudge his/her memory gently. I would simply remind him of the date of the deadline.
"A gentle reminder" is the phrase used to describe the way you politely remind someone; it is not the phrase you would actually say when delivering the reminder.
In the morning, I say to the professor: "I'm sure you won't forget to sign my form".
In the evening, I tell my friend: "This morning I gave the professor a gentle reminder to sign my form."