First, you may do an isolation test with only the phone plugged in directly (no filter/splitter) to check if there is noise on the line!
Then, you may also test with only the modem plugged in directly (no filter/splitter ... caution: phone unusable for this duration) to check if your SNR Margins improve considerably
Now, if there is no noise in first test and SNR margins improve a lot in the second test as compared to the 'normal' condition, then, you'll need to get a better filter/splitter (check reviews online if its a branded one ... and if you use multiple phones on same line, you'll need a filter for each 'extension')! Otherwise, you may register a complaint for noisy line!
Please note that some noise may still be there especially during sync! Also, power lines and other electrical equipment may induce noise in other lines/devices so try to isolate the modem with its separate power socket!