The picture above shows a marked increase in average check around the end of 2017 along with a big increase in discounting. Is this a strategy where discounts are being used to "soften the blow" of price increases? If so, that strategy seems to be mostly working. Notice that when the discounts decrease in early 2018, the average check retains much of the gain from the fall of 2017; it does not decrease in proportion to the decline in discounts. The same trend seems to be repeating in the first few weeks of 2019.
One conclusion that can be drawn from this data is that by combining an increase in discounts with a price increase, you could effectively increase your average check. While the market will ultimately determine how much the price of a menu item can increase, matching a higher discount when initially introducing a price increase appears to be an effective hedge.
Customers react to discounts differently across various types of restaurants, so using them may not be a good fit for a specific brand. However, if discounting is already part of your strategy, have they been increasing? Have you recently combined increased discounts when raising prices? What do your numbers say?