The json Text parameter was not valid JSON

Try to wrap your local!data[item] into integer. This will give you just the numbers and it will become an integer array. 

"""" & fv!item & """:[" & substitute(
  if(
    rule!GLB_isBlank(local!data[fv!item]),
    "",
    tointeger(local!data[fv!item])
  ),
  ";",
  ","
) & "]"

getting this output  "fieldName" :[∞]

Just a quick question. How are you getting this JSON? It looks like you are creating one by yourself. So why not directly use a!toJson on a map or dictionary?

I'm getting data from a CDT

That doesn't make sense. CDT doesn't have any data. It is the database that has it. And if you are getting data from DB, why do you need to involve JSON? 
Can you add the entire code snippet here?

a!localVariables(
  local!data: rule!xxxxxx(
    Id: 8
  ).data[1],
  local!keys: dictutil_getkeys(
    local!data
  ),
  local!listOfDifferences: a!forEach(
    items: local!keys,
    expression: if(fv!item = "yyyyy",
    """" & fv!item & """:[" & substitute(if(rule!GLB_isBlank(local!data[fv!item]), "", tointeger(local!data[fv!item])),";",",") & "]",
    """" & fv!item & """:""" & local!data[fv!item] & """"
    )
  ),
  a!fromJson(
    "{" & joinarray(
      local!listOfDifferences,
      ","
    ) & "}"
  )
)

What is the purpose of this code? Hand-crafting JSON is a bad idea in general.

What is the purpose of this code? Hand-crafting JSON is a bad idea in general.

setting up a parameter in webAPI

Any alternative that you'd want to suggest instead of Hand-crafting JSON?

Sure. Create a map and apply toJson().