What is the ruling on gifting a dog to a female friend who is ignorant of the ruling, and how can one expiate this sin after repentance, and does a qirat of reward diminish every day?

The fundamental rule regarding owning a dog is prohibition, except for a need deemed valid by Sharia. It is not permissible to gift a dog to someone who owns one without a [valid] need, because it constitutes aiding in a forbidden act.

Part of complete repentance is to strive to remove the effects of the forbidden act by advising your colleague, informing her of the Sharia ruling, and admonishing her to abandon owning it. If she does not respond after you have done your utmost, then you have fulfilled your obligation. Whoever repents from a sin and its effect remains, their repentance is accepted.