Why does Cersei keep telling Margaery she can "come to her with anything she needs"?

Question

I've been rewatching Game of Thrones recently, and I am really confused by this scene in S05E03 - "High Sparrow". It goes on for a couple minutes and I can't really make sense of it.

INT. ROOM

Cersei approaches a room with two guards. Inside, Margaery is having tea with some of her friends.

MARGAERY: I said, "Darling, surely 4 times is enough, are you trying to set a new record?" (Laughter). And he said, "Well, what is the record? I'm sure we can break it."

Margaery’s friends laugh. As Cersei walks in, they all get up and bow.

MARGAERY: Mother! (Gets up and hugs Cersei). Welcome.

CERSEI: Don't you look lovely. Marriage agrees with you.

MARGAERY: Can we bring you anything to eat or drink? I wish we had some wine for you. It's a bit early in the day for us.

CERSEI: No, no. I, I can't stay. I just wanted to let you know if, there is ever anything I can do for you.

MARGAERY: You are very sweet.

CERSEI: Tommen seems quite taken with his new queen.

MARGAERY: I absolutely adore him. You raised a gallant young man. I'm forever grateful.

CERSEI: Good. Good. I'm glad to hear you're happy.

MARGAERY: Ecstatic. I really am. Exhausted, to be honest, but what can I expect, he is half lion, half stag. (Margaery’s friends laugh).

CERSEI: I'll leave you to it then. (Turns to leave).

MARGAERY: Oh, forgive me, I haven't been at Court for long, I get so confused. What's the proper way to address you now? Queen Mother or Dowager Queen?

CERSEI: There's no need for such formalities.

MARGAERY: In any event, judging from the King's enthusiasm, the Queen Mother will be a Queen Grandmother soon.

CERSEI: Won’t that be a lovely day.

MARGAERY: Can you imagine the celebrations? They'll ring the bells all day and night.

CERSEI: Remember. Anything you need.

Margaery smiles. Cersei leaves. Margaery’s smile fades. It returns when her friends begin laughing, and she turns back around. Cersei walks away with her two guards, still able to hear the laughter.

The only thing going on seems to be Margaery reminding Cersei of her power waning. But what does Cersei mean with the "If there's ever anything I can do for you, just come to me", that she keeps reminding Margaery of? Obviously, she's not being genuine, but I just don't get it.

Answer 1

It's a subtle power play. The two are sparring with each other within the confines of decorum.

CERSEI: I just wanted to let you know if, there is ever anything I can do for you...

"Let me know if I can do anything for you," suggests Cersei is still the one in power, and if something needs to be done, it will be done through Cersei.

MARGAERY: Oh, forgive me, I haven't been at Court for long, I get so confused. What's the proper way to address you now? Queen Mother or Dowager Queen?

This is a slightly less subtle reminder that Cersei actually has no formal role in the governance of the realm. Her title of "Queen" was a ceremonial one, and now she is below Margaery in the picking order in that regard.

This is the same barb Keven Lannister threw in her face a few episodes earlier: "You are the Queen Mother. Nothing more." On that instance, Cersei justified her governance of the realm as being at Tommen's request.

Cersei Lannister : Uncle Kevan, in light of your position as commander of the Lannister armies, it would please the king for you to serve as his Master of War. No man living better deserves the title.

Kevan Lannister : That is kind of you to say. I would like to hear it from the king himself.

Cersei Lannister : The king is very busy at this moment.

Kevan Lannister : He should be here, learning what it means to rule.

Cersei Lannister : He is learning. On this occasion, in his capacity as ruler, he has asked me to speak on his behalf.

Kevan Lannister : I returned to the capital to pay my respect to my brother, and to you, and to serve the king. I did not return to the capital to serve as your puppet, to watch you stack the Small Council with sycophants. Sending your own brother away so you may...

Cersei Lannister : My brother has left the capital to lead a sensitive diplomatic mission.

Kevan Lannister : What mission?

Cersei Lannister : That is not your concern as Master of War.

Kevan Lannister : I do not recognize your authority to dictate what is and what is not my concern. You are the queen mother. Nothing more.

This is a key distinction from the books, where Tommen is much younger and Cersei is legally the Queen Regent and ruling on his behalf. In the show, Tommen is fully empowered as king and Cersei's rule is a matter of convention that he can end at any moment. Cersei is staking out her position that the marriage changes nothing, and Margaery is issuing a warning shot that her time of complete control over Tommen has ended.

Answer 2

My interpretation of this scene is that Cersei is trying to protect Tommen. Remember she just lost Joffrey and was devastated. Even though she thinks it was Tyrion, she is still worried if there might be any plots for Tommen.

She also knows that Margaery, and the Tyrell's at large, is playing the Game of Thrones. I believe she is trying to convince Margaery to come to her if she knows about any plots against Tommen, i.e., "If you need anything to help protect my son."

Cersei is hoping that above the manipulating facade that Margaery cares for Tommen even just a little a bit. Both Cersei and Margaery recognize that their power is directly tied to Tommen's even if they are both try to figure out a way to get around that...