@Caucasian Iberia - here are my sources - so make your mind.
https://en.wikipedia.org/wiki/David_Komnenos
For their assistance, David rewarded the Latin Empire with shiploads of corn and hams.Then, considering how Laskaris had encouraged Sultan Kay Khusrau I to besiege Trebizond in 1205 or 1206, David petitioned the Latin Emperor to include him as his subject in his treaties and correspondence with Laskaris, and to treat his land as Latin territory. In the words of William Miller, "It was his interest to prefer a nominal Latin suzerainty to annexation by the Nicaean emperor.
William Miller, Trebizond: The last Greek Empire of the Byzantine Era: 1204-1461, 1926 (Chicago: Agronaut, 1969), p. 17
Vassiliev commented that the lack of reference to David Komnenos in the Treaty of Nymphaeum (1214) was evidence that his former suzerain had no further use for him and abandoned him in order to gain a peace with Theodore.
A. A. Vasiliev, "The Foundation of the Empire of Trebizond (1204-1222)
http://www.jstor.org/stable/2846872
More recently the truth of his fate was rediscovered: a marginal note written at Mount Athos records David Komnenos died as a monk of Vatopedi monastery on 13 December 1212.
So from 1205/6 to 1212/3 Trebizond was vassal(client state) of the Latins not to Georgia.But this doesnt make Trebizond not to have trade and non aggression pact to simulate this with Georgia.
Georgia already got 3 vassals and in save position and no major enemies to the west and north,but the Latin Empire is fighting on 3 Fronts - Bulgaria,Epirus and Nicaea in 1212ad.1 Ally/vassal/client state will help the Latins and Trebizond to negate the rush of the 5 regioned Sultanate of Rum and the wars vs Bulgaria,Epirus and Nicaea.