Since you treat the 'sentence' (the 'predication' component of a clause, rather) as a TP, I assume you are broadly subscribing a late version of the Chomskian P&P theory of syntax, and, if so, there are multiple reasons why your tree is completely unacceptable, but I would not say the way you have represented the infinitive is a particularly important one. In that respect, if anything, your Chomskian syntax teacher could, perhaps, object that the lower 'T' should be 'Infl', rather than 'T', or 'T' but specified as [-Tense, -AGR], in opposition to the higher 'T', which should be marked as [+Tense, +AGR], but that's about it. That is not a serious defect, as far as I can see.
What is really wrong with your tree is that it reflects a strange hybrid theory in which a couple of Chomskian assumptions (the existence of the functional categories T and C as heads of the 'predication' and the 'clause', respectively) coexist with an otherwise traditional 'flat' early phrase structure-style account of everything else. That's why, no matter how you represent the infinitival element, there is no way to reconcile your tree with the late version of P&P Theory you seem to intend it to conform to.
I suppose you know that when Chomskian syntacticians like Pollock (and Chomsky himself) started analysing finite predications as TPs (around 1989), they continued to assume most of the results obtained within P&PT in the immediately preceding period, in particular a) Kayne's 'binary branching' hypothesis (1984)[which is incompatible with your analysis of the two TPs, the two VPs and the NP]; b) the three-tiered X-bar theory of Chomsky's Barriers (1986) [which clashes with the analysis your tree offers for absolutely all the phrasal categories involved]; c) Larson's 'shell' analysis (1988) [which is necessary to maintain Kayne's 'binary branching' hypothesis, but incompatible with Baker and the CP, or the two higher PPs in your tree being sisters]; d) the 'VP-Internal Subject Hypothesis' (1986-1988) [according to which Chomsky should initially be in the specifier of asked, a position you do not provide, as you generally fail to acknowledge specifiers]; e) Abney's (1987) 'DP Hypothesis' [which clashes with your NP label and your flat analysis of the 'NP' the changes to the theory]; and f) a highly elaborate view of the way arguments and adjuncts must be 'projected' and 'attached' in Comp X and Spec XP (or Adjunct X') [which is incompatible with your treating innocently as a sister of asked, Baker and the CP, and with the PP during the lecture being a sister of the verb comment and the PP on the changes to the theory]. Etc. Etc.
In short, no matter what aspect of your tree above is considered, it is hopelessly wrong for the theory of syntax you seem to want to work within, i.e., late P&P syntax (to judge from your use of 'TP'). Whether the infinitival inflection should be labelled 'I' or 'T'[-Tense, -AGR] is, in comparison, a very minor defect you need not worry about.