Learn English – What’s the meaning of “certain issues of conscience”

This should be answerable by dictionaries, and you should've been able to understand the whole phrase see through the veneer if you knew the meaning of see through and veneer.

Because see through (something) is a common phrase, I presume that you're not familiar with this sense of veneer (meaning, a cover or disguise). Here is the meaning of veneer in that sentence:.

veneer: [in singular] An attractive appearance that covers or disguises someone or something’s true nature or feelings:
'her veneer of composure cracked a little'

Just to cover the whole phrase, here is a definition of see through:

see through: Not be deceived by; detect the true nature of:
'he can see through her lies and deceptions'

So a wily interviewer is likely to see through the veneer means that it's likely that he or she will not be deceived or tricked by your cover or your pretending to know. They would see through your cover (read veneer). They would see through you. They would know better.

If you say

He acted a certain way.
He acted like a criminal.

you are describing exactly how he acted and your description is very accurate.

If you say

He acted in a certain way.
He acted in a suspicious way.
He acted in a criminal way.

you're description doesn't not nail down all the details to exactly describe how he acted, but you are saying he acted in a similar way to something, that his actions taken together makes him seem suspect.