Gatsby is sometimes called away to take these mysterious phone calls. They are quite real, and his secrecy about them and about his business dealings in general suggests that his income is derived from illegal sources. After Gatsby's death, Nick answers the phone one day at Gatsby's mansion and gets a glimpse of Gatsby's business dealings, as does the reader.
The call comes from Chicago, and as soon as Nick answers, someone who calls himself "Slagle" begins speaking excitedly, assuming he is talking to Gatsby himself:
Young Parke's in trouble . . . They picked him up when he handed the bonds over the counter. They got a circular from New York giving 'em the numbers just five minutes before. What d'you know about that, hey? You never can tell in these hick towns--
When Nick identifies himself, Slagle hangs up.
The content of Slagle's message reveals at least one of Gatsby's illegal business dealings. Someone named Parke apparently had tried to cash stolen bonds at a New York bank. The bonds had been stolen in some small town, but the numbers of the stolen bonds had been circulated to banks in the cities where they might be cashed. The numbers of the stolen bonds had arrived just minutes before Parke had tried to cash them in New York. Saying that Parke is "in trouble" most likely suggests that he has been arrested.
Gatsby does not fabricate long distance phone calls to impress his guests. The only person he wants to impress is Daisy so that she will return to him. The lavish parties he stages are intended to draw her to his mansion from her home in East Egg. Frequently Gatsby did not attend his own parties, and when he did, he kept a very low profile. In fact, the first time Nick meets Gatsby, Nick carries on a conversation with him for a while before realizing who he is.