How can I use grep to match but without printing the matches?

Use grep -q (quiet)

/var/folder/program.exe -L parameters |
grep -q "text_to_filter" && echo 'SomeText' > '/tmp/Log.txt'

As per man grep:

-q, --quiet, --silent Quiet; do not write anything to standard output. Exit immediately with zero status if any match is found, even if an error was detected. Also see the -s or --no-messages option.