The phrase "minimum threshold" refers to the lowest level or amount required for something to happen or be achieved. It indicates the bare minimum that is necessary for a particular condition or action to be met. Full definition
We have minimum thresholds in our mind that are a whole lot higher than government rates. (25iq.com)
If your income is more than the set minimum threshold, it's likely you'll be prompted to take a higher amount than you have applied for. (nation21loans.com)