How can you understand なんて.... ないですけど and other whole context?

Can everybody help me to inspect carefully those japanese
on how to translate into correct English from the context of manga ?
Please do not use the online google translator,

and then please translate correct English context
from their intonation and expression
thank for everyone's help

notably なんて喉元過ぎた後
なんで説得力ないですけど
I wonder the foreigner how to
translate this sentence in their country
I'm Taiwanese person

I'm so curious that foreigner how to translate them
Because I've never seen foreigner
traslating this manga

I think the なんで here is just spoken version of なので
As for なんて explanation, see this thread.