Information about the trace elements content of goose carcass parts with or without skin can be important for consumers when making dietary choices. This study aimed to (1) determine the effects of popular heat processing techniques on the content of chromium (Cr), iodine (I), manganese (Mn), and bromine (Br) in goose breast muscle, and (2) estimate the extent to which 100 g of goose meat—both with and without skin—cover the Nutrient Reference Values (NRV) for Cr, I, Mn, and the Tolerable Daily Intake (TDI) for Br in adults. The heat processing techniques used in the study were water bath cooking (WBC), Oven Convection Roasting (OCR), grilling (G), and pan frying (PF). Grilled goose breast without skin had the highest Br retention (97.4%) and TDI (2.41%). Cooked goose breast (WBC) with skin exhibited the highest retention of Cr (73.8%) and I (73.6%). The highest Mn content was found in meat without skin after OCR processing and grilled meat with skin (0.170 and 0.191 mg/100 g, respectively). The iodine content in the meat decreased (from 0.020 raw to 0.003 mg/100 g after PF) with each heat treatment. The results of our study may provide helpful information for consumers when making dietary choices and using heat treatment techniques. Goose breast muscles, depending on heat treatment and the presence of skin, provide trace elements in the range of 2.21% of NRV (Nutrient Reference Value) for Br without skin to 740.7% of NRV for Cr with skin and may be a valuable component of a varied diet (apart from iodine). The Br content in the meat decreases after WBC treatment (1.29 without skin or 1.43 with skin mg/100 g). For this reason, it seems to be the most beneficial for the consumer’s health because it minimizes the risk of exceeding the TDI value. Total hazard quotients (THQ) in meat (regardless of the treatment and skin presence) for Cr, Mn, and Br contents were <1, indicating a low risk to Polish consumer health.