Although your pension may be from Germany, as a U.S. resident, you are subject to taxation based on U.S. tax law. Tax treaties can override U.S. taxation, but most tax treaties' provisions don't apply to a U.S. resident's taxation by the U.S. This is referred to as the savings clause, as each country in the treaty "saves" the right to tax its own citizens and residents.
In limited circumstances, the treaty may help your U.S. tax situation. For example, if your German pension is similar in nature to U.S. Social Security income, then the U.S. would tax it in the same way the U.S. taxes Social Security benefits.
Although the savings clause of the treaty prevents you from reducing U.S. taxation, the treaty applies in reverse to minimize German taxation.
Under Article 18 of the treaty, the German pension should be exempt from German taxation since you are a resident of the U.S. Article 18 of the treaty states:
Subject to the provisions of Article 19 (Government Service; Social Security), pensions and other similar remuneration derived and beneficially owned by a resident of a Contracting State (U.S.) in consideration of past employment shall be taxable only in that State (U.S).
Accordingly, you should ask for an exemption from German taxes. You may have to submit certification of your U.S. tax status to the German taxation authorities to eliminate their taxation. You would do this by requesting certification on Internal Revenue Service Form 8802.
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