という as "said, called thus" is composed of
- the quoting particle と
- the verb 言う
The warrior (who is called) Arjuna is the protagonist of the Bhagavad Gītā.
Here the sentence アルジュナと言う modifies the noun 戦士, which is usually translated with a relative clause.
The sentence you quote is a little less straight-forward, but uses the same construction. Compare
That needs some improvements straight away.
That needs some improvements, but is not something to be done immediately.
The すぐに of the second (original) sentence refers to the immediacy of the need for improvements.
The long version would be
That needs some improvements, but it is not the case that we are dealing with something, which needs improvements straight-away.