I'd say yes. It may vary depending on your style and situation - but in the given example it's quite clear, imho, that what you called filter should be omitted.
A good rule could probably be: unless you want to point out some particular detail about the action ("I looked at it with a shocked expression/as if it were from another world/etc ...) the "filter" can be omitted.
It breaks the flow without adding relevant information: in the example you proceed describing the letter and your narrator takes the POV of your protagonist, so it's clear that he is looking.
Apart from this, the rule should be taken with a pinch of salt. As I mentioned it may vary on the situation. Personally I think that sentences as "What a day, he though" are allright, as long as they don't interrupt the stream of text too much, but that's pretty subjective.