Both operands in your last where clause are string. To compare dates, use the epoch formatted value.
| from datamodel:"TestTable"
| where scope LIKE "Test%"
| where us_schedule_state like "Accepted"
| where !LIKE(iteration, "%G")
| eval EndDate = strptime(AcceptedDate, "%Y-%m-%d")
| eval StartDate = strptime(trans_to_inprogress_date, "%Y-%m-%d")
| eval DateDiff = tostring((EndDate - StartDate), "duration")
| eval Date = strftime(1533096000.000000, "%Y-%m-%d %H:%S")
| where StartDate > strptime(Date, "%Y-%m-%d %H:%S")
OR simply
| from datamodel:"TestTable"
| where scope LIKE "Test%"
| where us_schedule_state like "Accepted"
| where !LIKE(iteration, "%G")
| eval EndDate = strptime(AcceptedDate, "%Y-%m-%d")
| eval StartDate = strptime(trans_to_inprogress_date, "%Y-%m-%d")
| eval DateDiff = tostring((EndDate - StartDate), "duration")
| eval Date = strftime(1533096000.000000, "%Y-%m-%d %H:%S")
| where StartDate > 1533096000.000000
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