Business Segment Information - Segment Reporting Information, by Segment (Details) $ in Thousands	7 Months Ended	12 Months Ended
	Aug. 16, 2021 restaurant	Jan. 02, 2022 USD ($)	Jan. 03, 2021 USD ($)	Dec. 29, 2019 USD ($)
Segment Reporting [Abstract]
Number of operating segments | restaurant	2
Segment Reporting Information [Line Items]
Depreciation and amortization		$ 20,600	$ 22,000	$ 22,200
Capital expenditures		19,528	18,369	41,247
Identifiable assets		367,113	568,743
Impairment and other lease charges		1,670	9,139	13,101
Continuing Operations
Segment Reporting Information [Line Items]
Revenues		357,277	315,358	363,473
Cost of sales		108,593	100,080	115,119
Restaurant wages and related expenses		91,669	74,328	84,909
Restaurant rent expense		23,592	22,773	22,050
Other restaurant operating expenses		57,430	47,823	50,274
Advertising expense		11,508	8,379	12,353
General and administrative expense		45,524	39,848	41,905
Adjusted EBITDA		25,016	25,991	39,971
Depreciation and amortization		20,574	22,009	22,186
Capital expenditures		13,026	10,483	23,122
Identifiable assets		367,113	400,242
Stock-based compensation		4,200	2,800	2,400
Impairment and other lease charges		1,538	8,023	15
Restaurant Wages And Related Expenses | Continuing Operations
Segment Reporting Information [Line Items]
Stock-based compensation		53	73	70
General and Administrative Expense | Continuing Operations
Segment Reporting Information [Line Items]
Stock-based compensation		4,163	2,681	2,320
Restaurant Sales | Continuing Operations
Segment Reporting Information [Line Items]
Revenues		355,492	314,112	361,693
Franchise Revenue | Continuing Operations
Segment Reporting Information [Line Items]
Revenues		1,785	1,246	1,780
Operating Segments
Segment Reporting Information [Line Items]
Impairment and other lease charges		1,538	8,023	15
Operating Segments | Pollo Tropical | Continuing Operations
Segment Reporting Information [Line Items]
Cost of sales		108,593	100,080	115,119
Restaurant wages and related expenses		91,669	74,328	84,909
Restaurant rent expense		23,592	22,773	22,050
Other restaurant operating expenses		57,125	47,354	49,768
Advertising expense		11,508	8,384	12,358
General and administrative expense		33,157	28,622	31,023
Adjusted EBITDA		36,802	36,517	50,560
Depreciation and amortization		19,962	21,112	21,476
Capital expenditures		12,424	9,163	21,921
Identifiable assets		310,972	311,905
Impairment and other lease charges		1,570	8,023	15
Operating Segments | Pollo Tropical | Restaurant Wages And Related Expenses | Continuing Operations
Segment Reporting Information [Line Items]
Stock-based compensation		53	73	70
Operating Segments | Pollo Tropical | General and Administrative Expense | Continuing Operations
Segment Reporting Information [Line Items]
Stock-based compensation		2,540	1,652	1,590
Operating Segments | Pollo Tropical | Restaurant Sales | Continuing Operations
Segment Reporting Information [Line Items]
Revenues		355,492	314,112	361,693
Operating Segments | Pollo Tropical | Franchise Revenue | Continuing Operations
Segment Reporting Information [Line Items]
Revenues		1,785	1,246	1,780
Other | Continuing Operations
Segment Reporting Information [Line Items]
Cost of sales		0	0	0
Restaurant wages and related expenses		0	0	0
Restaurant rent expense		0	0	0
Other restaurant operating expenses		305	469	506
Advertising expense		0	(5)	(5)
General and administrative expense		12,367	11,226	10,882
Adjusted EBITDA		(11,786)	(10,526)	(10,589)
Depreciation and amortization		612	897	710
Capital expenditures		602	1,320	1,201
Identifiable assets		56,141	88,337
Impairment and other lease charges		(32)	0	0
Other | Restaurant Wages And Related Expenses | Continuing Operations
Segment Reporting Information [Line Items]
Stock-based compensation		0	0	0
Other | General and Administrative Expense | Continuing Operations
Segment Reporting Information [Line Items]
Stock-based compensation		1,623	1,029	730
Other | Restaurant Sales | Continuing Operations
Segment Reporting Information [Line Items]
Revenues		0	0	0
Other | Franchise Revenue | Continuing Operations
Segment Reporting Information [Line Items]
Revenues		$ 0	$ 0	$ 0