Why there is no universal cleaning answer
Some manufacturers publish professional heat-exchanger cleaning procedures for particular models. For example, Lennox's EL297DFE service literature contains such a procedure. That establishes a model-specific service possibility, not permission to clean a different 40-year-old furnace or remove its tag. Lennox EL297DFE service literature, Cleaning Heat Exchanger.
We recommend asking the evaluator to show which manufacturer instruction applies to your furnace and what condition makes cleaning appropriate. If the recommendation is replacement, ask why a supported repair has not been established. The answer should address the condition, available parts, and the complete repair scope.
Do not wash the exchanger, take the furnace apart, reset safety controls, or remove the tag yourself. A service procedure involving fuel, venting, and internal components belongs with a qualified professional. The person who placed the restriction should explain what is required to clear it and who may do so.
Compare a real repair with a real replacement
Ask for the total proposed repair price and what checks follow the work. Compare that with a replacement's included equipment and installation work. Consider the remaining condition of the furnace and parts support, rather than treating age alone as either a replacement order or a reason to ignore the finding.
Manufacturer programs are also model-specific. Carrier's legacy secondary-exchanger program lists eligible models, serial numbers, dates, and repair or replacement conditions. It cannot be assumed to cover another brand or an older unit. Carrier legacy program.
The next step is the tag report and exact model. Those two records determine whether a supported repair exists. Until the restriction is properly resolved, plan for the furnace to remain off.