I'm curious about why the verb of the subject clause isn't using past tense.
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"Give" in that sentence is not a finite verb; it is an infinitive. So it doesn't inflect in the "primary tense system", and can be used with a main verb in the past tense just as well as it can be used with a main verb in the present tense.
The verb notice can take an infinitive clause as a complement. This construction doesn't seem to be recorded very well in the major online dictionaries; Collins has a small note mentioning this usage ("[Also V n inf]"), although it doesn't include any illustrative example sentence.
You could also say "I noticed (that) the shop owner gave the two women some cash." The meanings are similar, but to me, the construction with an infinitive has a more immediate feel, implying that the noticing occurred exactly at the point in time when the shop owner gave the cash.