The two initially seem to like each other, despite being adversarial. It is likely that the two enjoy having an intellectual equal. On Parson's side, Charlie is independent and one of the only characters who always seems to understand what Parson is saying, whether real world references or leetspeak is used. On Charlie's side, although Parson holds duty to Gobwin Knob, he is not bogged down by any of the prejudices Erfworlders generally have and has an out of the box method of thinking that Charlie can appreciate.
That said, however, considering the potential damage that Parson could do to him, having an intellectual equal is a "pleasure" which Charlie would forgo if he could. Charlie has informed Jillian that he's very concerned that his secrets have been compromised. The most damaging of the secrets about Charlie which Parson has learned so far would probably include:
1: One of Charlie's Rules instructs his Archons to make trouble for their own clients, in order to create new employment opportunities.
2: Charlie has no Warlords or Casters (or at least, none that the Archons know about).
3: Charlie never leaves the central tower of his city, which means potential assassins don't need to search the rest of the city to find him.
Fortunately for Charlie, Parson has yet to learn one of Charlie's most dangerous secrets; He is addicted to heroine buds and has been forced to use magical means to survive.
Charlie will certainly wonder how Parson could have survived the volcano. If he discovers that Parson entered the Magic Kingdom, he may suspect that Parson is a caster. Charlie appears to have discovered this by the time he briefs Tramennis in LIAB_43. He does not yet know Parson's discipline, suggesting to Tramennis that Parson is a Mathamancer, but he also confirmed to Parson himself that he can use scrolls.
By the Siege of Spacerock, it is revealed that Charlie is terrified of Parson. As the inventor of the very Summon Perfect Warlord Spell that summoned Parson in the first place, he is one of the few people capable of truly appreciating just how dangerous Parson actually is. There is a prophecy suggesting that Parson is Fated to defeat Charlie, and Charlie is thus determined to get Parson out of Erfworld by any means. Charlie arranges for Jojo to give Parson a scroll so that Parson can leave Erfworld peacefully but is ready to kill Parson if Parson refuses to leave.
Charlie, so far, has not worked against Parson directly, instead striking against Gobwin Knob's interests via proxies, such as Faq, Haggar, and Jetstone, likely to avoid the cataclysmic damage Parson could unleash if things escalate too much. He eventually reveals himself to Parson at the Siege of Spacerock, taunting him and telling Parson to "GTFO" (use the magic scroll Jojo gave him to leave Erfworld) or "DIAF" (die in a fire--specifically, the inferno consuming Spacerock)
After this incident, Parson feels similarly about Charlie and has allied with the Great Minds with the explicit goal of killing him.