putting a band around in order to gather what is inside together

Here the phrase means writers have shown an inclination quite often to pin their humour on Chinese characters.

In other words, Chinese characters have often been made the victim of the (misplaced) sense of humour of many writers.

Or writers have often cracked (silly?) jokes at the expense of Chinese characters.

bandy sth about/around phrasal verb [M]
to mention something often, without careful consideration or attention (from Cambridge dictionary)
AND

ban·dy [ bándee ]


transitive verb (past and past participle ban·died, present participle ban·dy·ing, 3rd person present singular ban·dies)

casually exchange words: to toss words back and forth casually, often without caring whether they are true or what effect they may have (from MSN Encarta Dictionary)

In your context, I think it is meaning 3 below that is appropriate (definitions from OED)

bandy

1 v.t. Throw, pass, strike (a ball) to and fro (as in tennis etc.). Chiefly fig. L16.

2 v.t. Cast away or aside; fig. dismiss or reject.

3 v.t. a Toss from side to side, from one to another, or about; esp. fig., pass (words, stories, etc.) around in a circle or group, discuss in this way.

b Give and take (blows, words, etc.); exchange (conversation, compliments, etc.) with a person.

4 v.t. (esp. refl.) & i. Band together, confederate.

5 v.i. Contend, fight. L16–E18.