The team _______ more than 300 runs in 20 overs _______ rain. However, some player needed to improve their batting skills.

The correct option is scored, despite.

Let's analyze the sentence structure and the usage of the blanks step-by-step to understand why this option is correct:

1. Analyzing the First Blank:
The sentence refers to a past event, indicated by the phrase "some player needed to improve their batting skills" (using the past tense verb "needed"). Therefore, the verb in the first blank must also be in the past tense to maintain grammatical consistency. Among the options, "scored" is the past tense form of the verb, while "score" is present tense and "scoring" is a gerund/present participle. Thus, "scored" is the correct fit for the first blank.

2. Analyzing the Second Blank:
The second part of the clause introduces a contrasting condition: "rain". The sentence implies that the team achieved the high run count even though it was raining. We need a preposition that expresses concession or contrast. Both "despite" and "in spite of" carry this meaning. However, since the first blank requires "scored", the only option that matches both grammatical requirements is "scored, despite".

3. Putting it all together:
Substituting "scored" and "despite" into the blanks, the sentence reads:
"The team scored more than 300 runs in 20 overs despite rain. However, some player needed to improve their batting skills."
This forms a grammatically correct and logically coherent sentence.