the parking inspector was sticking this on my windshield

Question

Man: What is it?

Woman: What does it look like? It's a ticket. I got a ticket. Well, read it.

Man: Overtime parking from 10 a.m. to 12:15 p.m. Ah, I don't understand.

Woman: Well, you're not allowed to park on the street for more than 2 hours. It's against the law.

Man: Well, did you park for more than 2 hours?

Woman: No. That's the whole point. I didn't park my car until 11 a.m. But when I got back, the parking inspector was sticking this on my windshield.

Man: Why?

Woman: He accuses me of parking in excess of 2 hours.

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"the parking inspector was sticking this on my windshield" Which tense is this sentence in?

Answer 1

It is the past continuous tense. Here it is used for placing a short action, "when I got back," into a longer background action, "...the parking inspector was sticking this on my windshield."

From a book on English grammar that I have written:

For interrupted action in the past, the quick action that interrupted the more prolonged action will be in the simple past, and the longer action will be in the past continuous tense. The short action may or may not stop the longer action. When, as, and while are often used to link the two clauses. If the sentence begins with a when, as, or while clause, we often use a comma to separate the clauses.

Note these:

I saw him when he was exercising in the park.
As he was exercising in the park, he fell.
While he was exercising in the park, she saw him.
We were checking in at the airport when I heard the explosion.
I was driving to the airport when he called me.
When I was driving to the airport, I saw a deer.

Answer 2

The Past continuous tense. It uses the past tense of the verb be and the –ing form of a verb.

It's explained here.