How to specify “does not contain” in dplyr filter

Note that %in% returns a logical vector of TRUE and FALSE. To negate it, you can use ! in front of the logical statement:

SE_CSVLinelist_filtered <- filter(SE_CSVLinelist_clean, 
 !where_case_travelled_1 %in% 
   c('Outside Canada','Outside province/territory of residence but within Canada'))

Regarding your original approach with -c(...), - is a unary operator that “performs arithmetic on numeric or complex vectors (or objects which can be coerced to them)” (from help("-")). Since you are dealing with a character vector that cannot be coerced to numeric or complex, you cannot use -.