I am assuming you are using the PebbleKit JS API. The appropriate doc is at: https://developer.getpebble.com/2/guides/javascript-guide.html
The doc says you can only send dictionaries with values as ints, strings, or byte arrays.
To send a list of strings, you have different options.
Send several key/value pairs, starting at a known index
{ 100: "MtGox", 101: "BitStamp", 102: "BTCChina" }
Send one string with a known separator and split it on the watch
{ "markets": "MtGox|BitStamp|BTCChina" }
Send an array of bytes with a list of keys that contain a market name
{ "markets": [100, 101, 102], 100: "MtGox", 101: "BitStamp", 102: "BTCChina" }