I understand that there is a need to be faithful to the Guru Mantra and that it should repeated it ceaselessly. How does one treat Special Purpose Mantras? Does one get “obligated” to a Deity after mantra takes effect (assuming that the Mantra is of a Higher Deity)? How does one safely thank the Deity of the Mantra and continue with the Guru Mantra. Is there a process?

Swamiji says:

There is only One God. Some times we call Him Creator, Protector, Transformer; He has many names, indicating the many functions He performs. Some times we call Him Her. She also has many names. So every name of God we call upon, is a name of the same God.

Therefore, there is no higher God or lesser God. There is no obligation to one form of divinity or to another form.
The reason we cultivate a special relationship with one form or another, is to create greater intimacy in that union.

There is no question of jealousy among the Gods.