You could match the field using ~
:
awk -F '\t' '$3==2 && $4 ~ /add|remove/' filename
would produce the desired result:
1 abc 2 word:add,word:remove text string
4 cncn 2 phone:add,phone: remove msg numeric
5 lmn 2 word:add msg text
Quoting from the manual:
~ !~ Regular expression match, negated match. NOTE: Do not use
a constant regular expression (/foo/) on the left-hand side
of a ~ or !~. Only use one on the right-hand side. The
expression /foo/ ~ exp has the same meaning as (($0 ~
/foo/) ~ exp). This is usually not what was intended.