What do you call an 'unselfish' action made with a selfish reason?

There are many examples of this, and I'd like to give a few:

• A person who puts a lot of effort to help the community and earns reputation points. But that reputation is the motivation behind helping the community, not because they really want to.
• A student approaches a professor, and helps them in their teaching and doing research in order to have a good LOR (letter of recommendation).
• To a SEO, the content of the website must be good (well, this one is a little tricky, but you get the spirit.)

I'm not saying that the reputation/LOR/high-ranked is not deserved. It is. I just want to focus more on the selfish reason(s) behind that.

_{Any kind of answer can be accepted: single word, phrase, proverb or idiom.}

Ulterior, as in, an ulterior motive. From the Collins dictionary:

if you say that someone has an ulterior motive for doing something, you believe that they have a hidden reason for doing it

While this doesn't necessarily define the action, it describes the reasoning/motivation behind it. To describe the action itself, you may describe the action as Ostensible, wherewith the actions you describe are ostensible, with ulterior motives

outwardly appearing as such; professed; pretended

The hidden agenda is a useful expression used to refer to the unsaid motives of somebody's actions:

• An undisclosed plan, especially one with an ulterior motive.(AHD)

While the terms supplied in the answer to Ooker's question are useful in describing "the reasoning/motivation behind" the action, neither of the single words ostensible nor ulterior apply solely to the question raised, i.e., doing/saying a "good" thing for "bad" or selfish reasons.

The opposite could be equally valid (often described as "the end justifying the means"): one might say/do a "bad" thing for reasons that redound ultimately to the common "good", and even these can said/done for selfish reasons! There is no real antonym for altruistic; selfish comes close but, alas, no.

The best idiom this contributor has come across to describe what Ooker is looking for is enlightened self-interest. No single word I can think of does the job. ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​ ​​​​​​​​​​​​​​​​​​​​​

In the study of religiousity, a person's orientation is classified as intrinsic, extrinsic, or quest. From this we can borrow the terms for motivation to behaviors as extrinsic (doing an outwardly selfless act for selfish reasons) or intrinsic (doing it selflessly).

In the context it's borrowed from, attending a church service could be intrinsic (for thinking about the religion) or extrinsic (to make friends, to keep up appearences).

To be clear, the term quest means to be continually searching for "truth" and may apply to someone who switches religions until they feel satisfied, or may discover their own (non-established) beliefs. It wouldn't apply as a third option to being selfish or unselfish.

Although she appeared to be genuinely interested in helping others, it later became evident all her actions were calculated and self-serving.