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Segment Reporting (Details) - USD ($)
$ in Thousands
 12 Months Ended
Dec. 31, 2023
Dec. 31, 2022
Dec. 31, 2021
Dec. 31, 2020
Segment Reporting Information [Line Items]        
Rental revenues $ 119,970 $ 116,491 $ 113,933  
Total revenues 831,068 909,402 896,167  
Gross profit (loss), by segment 111,703 114,785 121,923  
Interest expense 74,000 67,600 71,500  
Depreciation and amortization 35,630 37,952 39,885  
Goodwill and intangible assets, closure and other impairment charges 3,600 3,100 5,400  
Capital expenditures 37,200 35,300 16,800  
Goodwill 254,062 253,956 251,600 $ 251,600
Total assets 1,740,287 1,881,491 1,999,400  
Operating Segments        
Segment Reporting Information [Line Items]        
Gross profit (loss), by segment 396,700 377,300 375,200  
Goodwill 254,100 254,000 251,600  
Corporate        
Segment Reporting Information [Line Items]        
Gross profit (loss), by segment (285,000) (262,600) (253,300)  
Interest expense 70,000 60,700 63,300  
Depreciation and amortization 15,300 13,000 11,700  
Goodwill and intangible assets, closure and other impairment charges 300 0 0  
Capital expenditures 36,900 31,000 10,300  
Total assets 248,000 332,800 424,900  
Franchise operations        
Segment Reporting Information [Line Items]        
Revenue from contract with customer 706,365 662,438 631,936  
Company restaurants        
Segment Reporting Information [Line Items]        
Revenue from contract with customer 2,128 126,869 146,000  
Financing operations        
Segment Reporting Information [Line Items]        
Revenue from contract with customer 2,605 3,604 4,298  
Franchise operations | Operating Segments        
Segment Reporting Information [Line Items]        
Gross profit (loss), by segment 362,000 340,500 336,000  
Depreciation and amortization 9,800 10,000 10,100  
Goodwill and intangible assets, closure and other impairment charges 1,600 3,100 1,700  
Total assets 1,090,200 1,123,000 991,000  
Franchise operations | Franchise operations | Operating Segments        
Segment Reporting Information [Line Items]        
Revenue from contract with customer 706,400 662,400 631,900  
Goodwill 254,100 254,000 247,000  
Rental operations | Operating Segments        
Segment Reporting Information [Line Items]        
Rental revenues 120,000 116,500 113,900  
Gross profit (loss), by segment 32,500 28,500 26,100  
Interest expense 4,000 4,300 4,900  
Depreciation and amortization 10,500 10,700 11,100  
Total assets 375,300 390,600 426,600  
Company restaurants | Operating Segments        
Segment Reporting Information [Line Items]        
Gross profit (loss), by segment (0) 5,100 9,300  
Interest expense 0 2,600 3,300  
Depreciation and amortization 0 4,300 7,000  
Goodwill and intangible assets, closure and other impairment charges 1,700 0 3,700  
Capital expenditures 300 4,300 6,500  
Total assets 1,400 3,300 117,200  
Company restaurants | Company restaurants        
Segment Reporting Information [Line Items]        
Revenue from contract with customer 2,100 126,900    
Company restaurants | Company restaurants | Operating Segments        
Segment Reporting Information [Line Items]        
Revenue from contract with customer     146,000  
Goodwill 0 0 4,600  
Financing operations | Operating Segments        
Segment Reporting Information [Line Items]        
Gross profit (loss), by segment 2,200 3,200 3,800  
Total assets 25,400 31,800 39,700  
Financing operations | Financing operations | Operating Segments        
Segment Reporting Information [Line Items]        
Revenue from contract with customer $ 2,600 $ 3,600 $ 4,300