Learn English – Which verb should be used with injection – give or inject? What is the better way to talk about the injection

In this context, a "reminder" is a type of message, as is an invitation, a bill or a summons. If you remember this then it will be clear that, in the text of the reminder, you should use give. Referring to something you are likely to do in the future, send may be better.

To Bill:

• Have you billed him?
• No, I'll give him his bill now.
• I'm here to give you your bill.

To Invite:

• Have you invited him?
• No I'll give him his invitation now.

To Remind:

• Have you reminded him?
• No, I'll give him his reminder now.
• I'll send you a reminder later.
• This note is to remind you that...
• Hi! Just giving you that reminder I promised. Hope all is OK. Best etc.

You can of course also send, supply, provide or do any of the other things you do with messages, if it is appropriate to do so.

Gift is certainly used in this context - indeed, there is a cliche, a "god-given gift". Or "He thinks he's god's gift to women".

But blessing also seems natural and fine in your context, if perhaps a little old fashioned.