If you are in a character's Point Of View, Tom's, for example, and are seeing things that the character sees, then you don't need "Tom saw". Compare:
Tom saw a car come around a corner.
A car came around the corner.
If an omniscient narrator is talking, or another character, then there's a difference between the above statements. But if you are writing in a character's POV, there's no difference. "Tom saw" filters the perception. That is, it stands between the reader and the perception. It distances the reader from the action.
Same with "Tom felt". Compare:
Tom felt his arm itch.
Tom's arm itched.
Same with "Tom knew". Compare:
Tom wasn't looking. Tom knew there was no way she would be able to see it.
Tom wasn't looking. No way would she be able to see it.
Same with "Tom heard". Compare:
Tom heard the phone ring.
The phone rang.
If you are in character POV, then we know the character heard the phone because that's how we readers know it rang.
Same with "he remembered". Compare:
Tom surveyed the familiar scene. He remembered being here with his wife the day he met her.
Tom surveyed the familiar scene. Yes, he'd been here with his wife the day he met her.
Same with "Tom noticed". Compare:
Tom examined the letter. He noticed that the signature had been altered.
Tom examined the letter. The signature had been altered.
Some other filter words could be wondered, recalled, thought, realized. There are times when using filter words is appropriate. But more often than not, editors can strike them.
Especially if you are writing in limited POV, go through your manuscript and find all your filter words. Examine them carefully and see if you need them.