Actually - it's not Israeli influence. It's pro-Israel influence. Important difference. This includes lobby organisations funded or founded by wealthy Jews, conservative Christian lobbyists, pro-arms trade interests, and geopolitical interests (essentially Israel acts as a US military proxy they can use to keep the middle east in check). Not quite Israel secretly pulling strings (which is quite rightly dismissed as traditional boring anti-semetic conspiracy theory wearing a different hat), more of an alignment of interests, which dictator Netenyahu is currently taking advantage of to pursue his own career agenda (complete destruction of Iran and security of Israel from the mindset of a paranoid Israeli nationalist). Naturally, this involves attempting to buy out journalists and promote propaganda - and the Israeli attempts to do this are usually rather inept. What's far more effective is the already existing domestic pro-Israel lobby groups that have a completely above board, and vastly more effective way of funding Israel (and the vastly more powerful US military-financial-geopolitical interests).
Agree with your post. As a Jewish American, I have been advocating that it would be better for Americans and even Jews if we stop sending money to Israel and put political pressure on Israel to abandon illegal settlements, end the war on Gaza and work towards a resolution of the Israeli Palestinian conflict.
Unfortunately, this POV doesn't seem to be widely held by many woth influence.