Gave or Had given

[Dear life]

Hello everyone!
I'm having a tense problem.

Yesterday, my teacher asked me for a pen to sign the exam copies of students & I gave him one which, in a while he returned saying that something went wrong. At the time, I was writing my exam, so I couldn't check out what made him give the pen back to me. After returning to my room, I realized <why he gave/had given the pen back to me> <what might have happened when he gave/ had given the pen back to me>. I found the top of the pen stuck inside its cap. <——-Excess quote removed by moderator (Florentia52)——->

Could you please help me with the options I've given? I'm confused which one is the correct tense.

 

[Logos_]

First instance: had given (gave might also be acceptable here but had given is better). Second instance: gave.

 

[Dear life]

Thank you Logos