Not sure if I fully understand your question. Do you want to remove single quotes from the beginning and end and remove $ from the end? If so, you can use this ...
importTabs.Add(row["TABLE_NAME"].ToString().TrimEnd('$').Trim('\''))
If the $ sign is in front of the final tic label, then Trims must be reversed ...
importTabs.Add(row["TABLE_NAME"].ToString()).Trim('\'').TrimEnd('$')
If you know that there is no $ sign at the beginning, you can simplify it ...
importTabs.Add(row["TABLE_NAME"].ToString().Trim('$', '\''))
If you want to pass it as a parameter, Trim takes an array of characters
char[] charactersToRemove = new[] {'$', '\''}; importTabs.Add(row["TABLE_NAME"].ToString().Trim(charactersToRemove))
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