It's not a particularly significant choice, but using the continuous form adds a stronger nuance of "immediacy". That's to say the temporal frame suggested by such statements tends to include the present as well as the future. If we contrast them...
1a: I will not be giving Donald Trump a chance.
1b: I will not give Donald Trump a chance.
2a: I won't be giving a little reset button like Hillary
2b: I won't give a little reset button like Hillary
...then in #1a it's more a matter of the speaker telling us what her position is in relation to Trump, whereas in #1b she's talking about what she will or won't do in the future.
Even more specifically, in #2a Trump is bringing up something Clinton is doing right now, as opposed to #2b ...like Hillary [did, in the past].
Connective prepositions before, after, when, while, as soon as, etc. may be added to a clause to express that a second activity occurs earlier than, later than or at the same time as the activity in the main clause.
If the verb in the main clause is present tense, the verb in clause following the preposition is also present.
After we finish our homework, we go for a walk. (later then, as we
usually do)
Connective prepositions may also be added to a clause with a future tense verb expression such as will or (be) going to. In this case, the verb in the clause following the connective preposition does not change tense. It remains in present tense form.
After we finish our homework, we'll go for a walk. (later then, today)
So, the correct choice will be
It will be delivered after it is inspected. (first it will be inspected then delivered)
The difference between variants A, B, and C is that only variant A is grammatically correct.
Best Answer
I disagree with @user3169. I would never use B with my boss, I think it has a very privileged tone. Will is very direct and implies that it is what is going to happen no matter what. With my boss I would always go for a less commanding tone, like that of A, or something even more passive like:
Which implies that it's out of your control, instead of B which implies that you made the decision yourself.